Multi-carrier communication system and receiver thereof

ABSTRACT

The present invention is a multi-carrier communication system for transmitting/receiving signals via at least four sub-channels, comprising: a transmitter for transmitting data independently via the four sub-channels; a receiver comprising a receive unit disposed for each sub-channel for receiving data from a corresponding sub-channel and performing soft decision of the receive data; and means for inputting soft decision target values in receive units corresponding to three sub-channels other than a target sub-channel to a receive unit of the target sub-channel, wherein the receive unit of the target sub-channel adjusts its own soft decision target value using the soft decision target values that are input from the receive units of the other sub-channels, and decides the receive data based on this adjusted soft decision target value.

This application is a continuing application, filed under 35 U.S.C.§111(a), of International Application PCT/JP03/00950, filed Jan. 31,2003.

BACKGROUND OF THE INVENTION

The present invention relates to a multi-carrier communication systemand a receiver thereof, and more particularly to a multi-carriercommunication system using the interference between a target sub-channeland two or more upper and lower sub-channels (ICI) and a receiverthereof.

The bit error rate (BER) of the multi-carrier communication system infilter bank modulation, DMT modulation and FMT modulation can beimproved by using receive signals that include distortion byinter-channel interference (ICI). Inter-channel interference occurs bythe malfunction of a system in communication systems, such as OFDM-CDMA,or due to an unavoidable environment such as the loss of orthogonalitybetween sub-channels. Inter-channel interference, which is called the“leak of spectrum energy”, at times the cross-talk between sub-channels,is caused by a leak.

A major advantage of the turbo receiver of the present invention is thatthe phenomenon of ICI is handled as a zero mean Gaussian distributionrandom variable (e.g. Gaussian approximation used in the followingdocument 1 below), for which a finite state discrete Markov processmodel is used. For such an ICI model, simple Gaussian approximationseems to be more practical because of the nature of ICI. The turboreceiver of the present invention is based on a maximum posteriorprobability estimation algorithm. In this turbo receiver, informationderived from one sub-channel after non-linear processing refines theestimated maximum posterior probability of the latter channel, and inthe same way, the information derived from the other sub-channel refinesthe estimated maximum probability of the former sub-channel.

Document 1: K. Sathanathan and C. Tellambura: “Probability of errorcalculation of OFDM system with frequency offset”, IEEE Trans. Commun.,Vol. 49, NO. 11, November 2001, pp. 1884-1888.

(a) Relationship Between Frequency Offset and ICI

In the case of a multi-carrier communication system where a band isdivided into a plurality of sub-bands, which are independent narrowbands, and the transmission data of each sub-band isfrequency-multiplexed and transmitted and received, the selection of afilter set in a multi-carrier communication system for filter bankmodulation, DMT (Discrete Multi-tone) modulation and FMT (FilteredMulti-tone) modulation, has been executed under the constraint thatinter-symbol interference (ISI) and inter-channel interference (ICI) arecompletely removed.

In an ideal transmission channel where there is no Doppler shift andwhere there is no offset frequency between transmitter/receiver andsignal distortion does not occur, this constraint guarantees thereceiver that the recovery of transmission symbols to be error free.However the frequency offset which is generated in each channel, due toinaccurate tuning of the oscillator and the Doppler shift, causes BERdeterioration due to a spectrum leak or ICI.

The only method to relax such deterioration of BER is to minimize thefrequency offset, and more particularly, to maintain it to be within 1%of the sub-carrier frequency interval. This method, however, requiresaccurate frequency offset estimation, and also if the noise level ishigh when multi-carrier signals mixed with noise are received, theaccuracy of frequency offset estimation is affected. Also according tothis method, the Doppler shift is not consistent with respect to thetransmission symbols in a high-speed fading channel, and operationbecomes inaccurate in a high-speed fading channel which changesdepending on the time.

Here the case of a DMT base system and an ideal white Gaussian noise(AWGN) channel is assumed. It is also assumed that the level ofinter-symbol interference ISI can be ignored compared with theinter-channel interference ICI and other noise signals. To simplifydescription, only a target channel, the first adjacent sub-channellocated below the target sub-channel and the second adjacent sub-channellocated above the target sub-channel, are considered. FIG. 1 and FIG. 2show the frequency response of the three channels in the case when thefrequency offset is zero (FIG. 1), and in the case when the frequencyoffset is not zero (FIG. 2). The signals of the central frequencies f₁,f₂ and f₃ corresponding to the first, second and third sub-channels areindicated by the vertical arrows in FIG. 1 and FIG. 2. In FIG. 1 andFIG. 2, the sub-channel number 0 (ch0) indicates the target sub-channel,the sub-channel number −1 (ch−1) is a sub-channel located below thetarget sub-channel in the frequency scale, and the sub-channel number +1(ch+1) indicates the sub-channel located above the target sub-channel inthe frequency scale. If the cycle of the DMT symbol is T, then thefrequency scale is normalized with a channel interval equal to 1/T. Inother words, one unit of the frequency scale is the channel interval. AsFIG. 1 shows, when the frequency offset (normalized by the channelinterval) α is 0, the transfer function of the lower sub-channel and theupper sub-channel, indicated by the solid line A and the dotted line Bin FIG. 1, gives infinite attenuation in the central frequency f₂ of thetarget sub-channel (dotted line C). In the same way, the transferfunction of the target sub-channel gives infinite attenuation in thecentral frequencies f₁ and f₃ of the lower and the upper sub-channels.In other words, if the frequency offset α is zero, ICI is not generatedbetween adjacent sub-channels. This means that if the frequency offsetis zero, the respective sub-channels intersect orthogonally, and ICIdoes not exist at all.

If the frequency offset α is not zero, however, the orthogonality of thesub-channels is affected, and ICI is generated. FIG. 2 shows thespectrum characteristics of each sub-channel of the DMT system when thefrequency offset α is not zero. The spectrum of adjacent channels crossat −3 dB, and the first side-lobe is −13 dB, which is high. In order toavoid a complex system model, the case when the sub-channels which aredistant for a 1 or 2 channel interval interfere with each other will beconsidered below. It is clear that the spectrum of an adjacentsub-channel has a mutual gain which is not zero, which is indicated asα₀₋₁, α₁₋₁, α₁₀, α⁻¹⁰, α₀₁ and α⁻¹¹. In these notations the first indexof a indicates the interference source sub-channel, and the second indexindicates the interference target sub-channel. In other words, α⁻¹⁰indicates the leak transfer coefficient (amplitude) from the lowersub-channel with the sub-channel number −1 to the target channel withthe sub-channel number 0. α⁻¹¹ indicates the leak transfer coefficient(amplitude) from the lower sub-channel with the sub-channel number −1 tothe upper sub-channel with the sub-channel number 1, α₀₁ indicates theleak transfer coefficient from the target sub-channel with thesub-channel number 0 to the higher sub-channel with the sub-channelnumber 1, α₀₋₁ indicates the leak transfer coefficient from the targetsub-channel with the sub-channel number 0 to the lower sub-channel withthe sub-channel number −1, and α₁₀, indicates the leak transfercoefficient from the higher sub-channel with the sub-channel number +1to the target sub-channel with the sub-channel number 0. As describedabove, if the frequency offset α is not zero, the mutual gain which isnot zero, that is ICI (cross-talk), is generated between sub-channels.

(b) General Model of Communication System

FIG. 3 is a general model (four sub-channel model) depicting the mutualICI of four sub-channels in a DMT system having frequency offset.Compared with the three sub-channel model (see FIG. 4), according to theturbo receiver of the present invention, the four sub-channel model canimprove the total system BER in more cases because of the low roll offspectrum characteristics of DMT. 1₁, 1₂, 1₃ and 1₄ are the transmittersof the sub-channels ch−1, ch0, ch+1 and ch+2, 2₁, 2₂, 2₃ and 2₄ are thereceivers of each sub-channel, 3₁, 3₂, 3₃ and 3₄ are the transmissionlines of each sub-channel. 4_(ij) is a multiplier to multiply thesub-channel signal D_(i) by the leak transfer coefficient (interferencecoefficient) α_(ij) of the sub-channel with the number i to thesub-channel with the number j respectively, 5₁, 5₂, 5₃ and 5₄ are thefirst synthesizing units for synthesizing the cross-talk (ICI) from theadjacent sub-channel to its own sub-channel signal, 6₁, 6₂, 6₃ and 6₄are the second synthesizing units for synthesizing the cross-talk (ICI)from the sub-channel which is distant from two channel intervals to itsown sub-channel signal, and 7₁, 7₂, 7₃ and 7₄ are the noise synthesizingunits.

As FIG. 3 shows, the signals from the lower sub-channel ch−1 leak intothe target sub-channel ch0 via the cross-talk coefficient α⁻¹⁰, thesignals from the upper sub-channel ch+1 leak into the target sub-channelvia the cross-talk coefficient α₁₀, and the signals from the uppersub-channel ch+2 leak into the target sub-channel ch0 via the cross-talkcoefficient α₂₀. Also the signals from the lower sub-channel ch−2 leakinto the target sub-channel via the cross-talk coefficient α⁻²⁰, butdescription thereof will be omitted since this can be regarded as thesame as the leak from the ch+2. In the model in FIG. 3, the sub-channelsthat cause mutual interference are limited to the upper and lowersub-channels, but the number of sub-channels in the entire communicationsystem is not limited, so the model in FIG. 3 can also be applied to amulti-carrier communication system that has N number of sub-channels,where N is 4 or a greater number. In such a case as well, interferenceto each sub-channel is only from the lower two sub-channels and theupper two sub-channels. In this case, the interference coefficientindicates a chain of coefficients. The noise components denoted asn₁(t), n₂(t), n₃(t) and n₄(t) in FIG. 3 are statistically independent(no correlation) because of the frequency orthogonality between thesub-channels.

The sub-channels are located in the frequency domain, but this model canbe applied not only to a DMT modulation type or a filter bank modulationtype system, but also to other systems. The dimensions can be expandedto other domains, such as space (space division multiplex axis) andpolarity.

(c) Technical Problem

The model in FIG. 3 is beneficial in terms of understanding the physicalprocess which causes ICI. The problem of this model lies in accuratelydeciding the receive signals of each sub-channel and the value of thetransmission information symbols (a sign if a binary number).

One possible method to reduce ICI in a receiver is applying the decisionfeedback equalizer (DFE) to cancel ICI, which is proposed in thefollowing document 2.

Document 2: Viterbo and K. Fazel, “How to combat long echoes in QFDMtransmission schemes: Sub-channel equalization or more powerful channelcoding,” Proc. IEEE Globecom '95, Singapore, November 1995, pp.2069-2074.

If the output of an individual receiver is in hard bit decision (harddecision) format, then sharing information among sub-channels has only afew benefits. This restricts the operation range of DFE which uses ahard decision.

The above mentioned approach is effective in many practical cases, butis for minimizing the effect of ICI, and is the second best approach.Since ICI includes information on transmission symbols, it is possibleto remodulate the receive signals quite well by using this transmissionsymbol information included in ICI.

SUMMARY OF THE INVENTION

With the foregoing in view, it is an object of the present invention toimprove BER performance using the ICI in a communication system whereICI exists.

It is another object of the present invention to decrease BER based onthe posterior probability using ICI.

The present invention is a multi-carrier communication system fortransmitting/receiving signals via at least four sub-channels,comprising a transmitter for transmitting data independently via fourchannels, a receiver comprising a receive unit disposed for eachsub-channel for receiving data from a corresponding sub-channel andperforming soft decision of the receive data, and means for inputtingsoft decision target values in the receive units corresponding tosub-channels other than a target sub-channel to a receive unit of thetarget sub-channel, wherein the receive unit of the target sub-channeladjusts its own soft decision target value using the soft decisiontarget values that are input from the receive units of the othersub-channels, and decides the receive data based on the adjusted softdecision target value.

The receive unit of the target sub-channel further comprises means forcomputing a difference between a probability that the data received fromthe target sub-channel is one value of a binary and a probability thatthe data is the other value of a binary as the soft decision targetvalue, considering degree of coupling of cross-talk paths, means foradjusting the soft decision target value of the target sub-channel usingthe soft decision target values that are input from the receive units ofthe other sub-channels, and a decision unit for deciding the receivedata based on adjusted the soft decision target value.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the frequency characteristics when the frequency offset iszero;

FIG. 2 shows the frequency characteristics when the frequency offset isnot zero;

FIG. 3 shows a general model for depicting the mutual ICI of fourchannels in a DMT system having frequency offset;

FIG. 4 is a general block diagram depicting a communication system thatdemodulates receive data using the interference between lower onesub-channel and upper one sub-channel;

FIG. 5 is a block diagram depicting a receiver of a three sub-channelmodel;

FIG. 6 is a general block diagram depicting a communication system fordemodulating receive data using the interference between lower onesub-channel and upper two sub-channels, which shows the case where thenumber of sub-channels is 4 (four sub-channel model);

FIG. 7 is a first block diagram depicting a receiver in the case whenthe cross-talk from upper two sub-channels and lower one sub-channelexist, and indicates the configuration of the left side of the receiver;

FIG. 8 is a second block diagram depicting a receiver in the case whenthe cross-talk from upper two sub-channels and lower one sub-channelexist, and indicates the configuration of the right side of thereceiver;

FIG. 9 is a diagram depicting the constellation of the targetsub-channel according to the number of repeats according to the turboreceiver of the present invention;

FIG. 10 is a characteristic diagram depicting the average BERperformance of the turbo receiver of the present invention and aconventional matched filter base receiver;

FIG. 11 is a block diagram depicting a DMT base communication systemusing the turbo receiver of the present invention; and

FIG. 12 is a characteristic diagram depicting the BER performance of theDMT receiver having the turbo processing function of the presentinvention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

(A) General Configuration of Communication System in the Case of ThreeSub-Channels

FIG. 4 is a general block diagram depicting a communication system thatdemodulates receive data using the interference between a total of twosub-channels, lower and upper, and is a case when the number ofsub-channels is three. The intent of the present invention is to providea communication system having at least four sub-channels (foursub-channel model), but a communication system having three sub-channels(three sub-channel model) will be described first to assist inunderstanding the present invention.

The communication system in FIG. 4 comprises three transmitters, 21, 22and 23, for transmitting data independently via the three sub-channels,ch−1, ch0 and ch+1 respectively, many cross-talk paths 31 _(ij) having acoupling coefficient α_(ij) to the i-th to the j-th sub-channel, threereceivers, 40, 50 and 60, which are installed for each sub-channel forreceiving data from the corresponding sub-channel and performing thesoft decision of the receive data, and means 71 and 72 for inputting thesoft decision target value of each receiver to another receiver. 32-34and 35-37 are synthesizing units for synthesizing ICI signals and noise.

The receiver 50 of the sub-channel ch0 adjusts its own soft decisiontarget value using the soft decision target values which were input fromthe receivers 40 and 60 of the lower and upper sub-channels ch−1 andch+1, and decides “0” or “1” of the receive data based on the softdecision target value. In the same way, the other respective receiversadjust its own soft decision target value using the soft decision targetvalues which were input from the receivers of the lower and uppersub-channels, and decides “0” or “1” of the receiver data based on thesoft bit decision target value.

(B) Algorithm of Receive Symbol Demodulation in Three Sub-Channels

An algorithm for the receiver of the target sub-channel ch0 todemodulate the receive signals in the communication system shown in FIG.4, will be described.

The principle of the demodulation algorithm is to derive the value InD₀which indicates the difference of the posterior probability P(D₀=+1/y(t)) of the information symbol received by the targetsub-channel ch0 becoming “0” (=+1) and the posterior probability P(D₀=−1/y(t)) of this becoming “1” (=−1). This is because if thedifference InD₀ of the posterior probability can be derived, it can bedecided whether the receive information symbol is “0” or “1”. In otherwords, the probability difference InD₀ of the target sub-channel is thedifference between the posterior probability P (D₀=+1/y(t)) of thereceive information symbol becoming “0” (=+1), and the posteriorprobability P (D₀=−1/y (t)) of this becoming “1” (=−1), so if InD₀>0,then the receive information of the target sub-channel is “0”, and ifInD₀<0, then the receive information of the target sub-channel isdecided as “1”. According to the above, the value InD₀ to indicate thedifference of the posterior possibility, is derived.

It is assumed that the binary information is transmitted as the signalS*_(ij) (t) via the two adjacent sub-channels. The index i of S*_(ij)(t) is determined by the sign of the information symbol D_(i)(i=−1, 0or 1) in sub-channel i. In other words,if D_(i)=+1, then j=0if D_(i)=−1, then j=1  (1)Hereafter to simplify notation, the time dependency of S*_(ij) (t) inexpressions is omitted. In other words, S*_(ij) (t) is denoted asS*_(ij).

It is assumed that the transmission information symbol D_(i) isstatistically independent (no correlation) and is an equally distributedprobability variable. As FIG. 4 shows, the signal of the targetsub-channel affected by ICI from the lower and upper sub-channels isexpressed as the linear coupling of the signals S*_(−1j) and S*_(1j)transmitted by the upper and lower sub-channels and the target channelsignal S*_(0j) by the cross-talk coefficient α. The cross-talkcoefficient α is a value according to the leak of cross-talk. If theinformation symbol D₀ of the target channel is +1, then the receivesignal S_(j) (j=0-3) of the target channel becomes

$\begin{matrix}\left\{ \begin{matrix}\begin{matrix}{{S_{0} = {S_{00}^{*} + {\alpha_{- 10} \cdot S_{- 10}^{*}} + {\alpha_{10} \cdot S_{10}^{*}}}},} & {{D_{0} = {+ 1}},{D_{- 1} = {+ 1}},{D_{1} = {+ 1}}}\end{matrix} \\\begin{matrix}{{S_{1} = {S_{00}^{*} + {\alpha_{- 10} \cdot S_{- 10}^{*}} - {\alpha_{10} \cdot S_{10}^{*}}}},} & {{D_{0} = {+ 1}},{D_{- 1} = {+ 1}},{D_{1} = {- 1}}}\end{matrix} \\\begin{matrix}{{S_{2} = {S_{00}^{*} - {\alpha_{- 10} \cdot S_{- 10}^{*}} + {\alpha_{10} \cdot S_{10}^{*}}}},} & {{D_{0} = {+ 1}},{D_{- 1} = {- 1}},{D_{1} = {+ 1}}}\end{matrix} \\\begin{matrix}{{S_{3} = {S_{00}^{*} - {\alpha_{- 10} \cdot S_{- 10}^{*}} - {\alpha_{10} \cdot S_{10}^{*}}}},} & {{D_{0} = {+ 1}},{D_{- 1} = {- 1}},{D_{1} = {- 1}}}\end{matrix}\end{matrix} \right. & (2)\end{matrix}$depending on whether the signals D⁻¹ and D₁ of the lower and uppersub-channels are +1 or −1. j of the signal S_(j) indicates the signalnumber. In the same way, if the information symbol D₀ of the targetchannel is −1, then the receive signal S_(j) (j=4-7) of the targetchannel becomes

$\begin{matrix}\left\{ \begin{matrix}{{S_{4} = {{{- S_{00}^{*}} + {\alpha_{- 10} \cdot S_{- 10}^{*}} + {\alpha_{10} \cdot S_{10}^{*}}} = {- S_{3}}}},{D_{0} = {+ 1}},{D_{- 1} = {+ 1}},{D_{1} = {+ 1}}} \\{{S_{5} = {{{- S_{00}^{*}} + {\alpha_{- 10} \cdot S_{- 10}^{*}} - {\alpha_{10} \cdot S_{10}^{*}}} = {- S_{2}}}},{D_{0} = {+ 1}},{D_{- 1} = {+ 1}},{D_{1} = {- 1}}} \\{{S_{6} = {{{- S_{00}^{*}} - {\alpha_{- 10} \cdot S_{- 10}^{*}} + {\alpha_{10} \cdot S_{10}^{*}}} = {- S_{1}}}},{D_{0} = {+ 1}},{D_{- 1} = {- 1}},{D_{1} = {+ 1}}} \\{{S_{7} = {{{- S_{00}^{*}} - {\alpha_{- 10} \cdot S_{- 10}^{*}} - {\alpha_{10} \cdot S_{10}^{*}}} = {- S_{0}}}},{D_{0} = {+ 1}},{D_{- 1} = {- 1}},{D_{1} = {- 1}}}\end{matrix} \right. & (3)\end{matrix}$depending on whether the signals D⁻¹, and D₁ of the lower and uppersub-channels are +1 or −1.

After introducing ICI, S_(j) (j=0, 1, 2, . . . 7) is used as eightsignals in the input of the receiver of each sub-channel. The index j ofS_(j) in the expressions (2) and (3) indicates the signal number, and isdetermined by airing the symbols D⁻¹, D₁ and D₀ in the lowersub-channel, upper sub-channel and target sub-channel.

By considering the following [1] and [2], an algorithm for optimumreception can be further developed. In other words, by considering [1]that the signs of some information signals are the opposite, that is−S*⁻¹⁰=−S*⁻¹¹, S*₀₀=−S*₀₁, and S*₁₀=−S*₁₁, and [2] to transmitinformation symbols a same signal is used for the lower and uppersub-channels and target sub-channel, that is S*⁻¹⁰=S*₀₀=S*₁₀, andS*⁻¹¹=S*₀₁=S*₁₁, the algorithm for optimum reception can be furtherdeveloped. The latter [2] indicates that all the sub-channels have thesame value and the information signals of all the sub-channels have nodifference in amplitude, waveform and energy. In this case the signalsof the expressions (2) and (3) in each sub-channel become a pair, havingopposite signs, as shown in the following expressions.

$\begin{matrix}\left\{ \begin{matrix}{S_{0} = {{S_{00}^{*} + {\alpha_{- 10} \cdot S_{- 10}^{*}} + {\alpha_{10} \cdot S_{10}^{*}}} = {- S_{7}}}} \\{S_{1} = {{S_{00}^{*} + {\alpha_{- 10} \cdot S_{- 10}^{*}} - {\alpha_{10} \cdot S_{10}^{*}}} = {- S_{6}}}} \\{S_{2} = {{S_{00}^{*} - {\alpha_{- 10} \cdot S_{- 10}^{*}} + {\alpha_{10} \cdot S_{10}^{*}}} = {- S_{5}}}} \\{S_{3} = {{S_{00}^{*} - {\alpha_{- 10} \cdot S_{- 10}^{*}} - {\alpha_{10} \cdot S_{10}^{*}}} = {- S_{4}}}}\end{matrix} \right. & (4)\end{matrix}$From the expression (2), (3) and (4), the posterior probability toreceive the signal S_(j), that is the posterior probability P (S_(j)/y(t)) of the receive signal becoming S_(j), is given by the followingexpression.

$\begin{matrix}{{P\left\lbrack {S_{j}/{y(t)}} \right\rbrack} = {{k_{0} \cdot {P_{apr}\left( S_{j} \right)} \cdot {P\left( {{y(t)}/S_{j}} \right)}} = {{k_{0} \cdot {P_{apr}\left( S_{j} \right)} \cdot \exp}\left\{ {{- \frac{1}{N_{0}}}{\int_{0}^{T}{\left\lbrack {{y(t)} - S_{j}} \right\rbrack^{2}\ {\mathbb{d}t}}}} \right\}}}} & (5)\end{matrix}$where

-   -   k₀ is a normalized factor    -   j is a signal number (j=0, 1, . . . 7),    -   y(t) is a synthesized signal (y(t)=S_(j)+n(t)) of the signal        series S_(j) involving ICI and the white Gaussian noise n(t)        having the spectrum power intensity N₀,    -   P_(apr) (S_(j)) is a prior probability of the receive signal        S_(j), and    -   P (y(t)/S_(j)) is a conditional probability, and is a        probability where the transmitted sign signal is S_(j) when the        receive signal is y(t).

In the prior probability P_(apr) (S_(j)) (j=0, 1, . . . 7) is expressedas a cross-product of the prior probability of the signal of the targetsub-channel becoming S*₀₀ or S*₀₁ and the posterior probability of theinformation signal S*_(ij) in the two adjacent sub-channels. In otherwords, if D₀=+1, the prior probability P_(apr) (S_(j)) becomes

$\begin{matrix}\left\{ \begin{matrix}{{P_{apr}\left( S_{0} \right)} = {{P\left( S_{- 10}^{*} \right)} \cdot {P_{apr}\left( S_{00}^{*} \right)} \cdot {P\left( S_{10}^{*} \right)}}} \\{{P_{apr}\left( S_{1} \right)} = {{P\left( S_{- 10}^{*} \right)} \cdot {P_{apr}\left( S_{00}^{*} \right)} \cdot {P\left( S_{11}^{*} \right)}}} \\{{P_{apr}\left( S_{2} \right)} = {{P\left( S_{- 11}^{*} \right)} \cdot {P_{apr}\left( S_{00}^{*} \right)} \cdot {P\left( S_{10}^{*} \right)}}} \\{{P_{apr}\left( S_{3} \right)} = {{P\left( S_{- 11}^{*} \right)} \cdot {P_{apr}\left( S_{00}^{*} \right)} \cdot {P\left( S_{11}^{*} \right)}}}\end{matrix} \right. & (6)\end{matrix}$and if D₀=−1, the prior probability P_(apr) (S_(j)) becomes

$\begin{matrix}\left\{ \begin{matrix}{{P_{apr}\left( S_{4} \right)} = {{P\left( S_{- 10}^{*} \right)} \cdot {P_{apr}\left( S_{01}^{*} \right)} \cdot {P\left( S_{10}^{*} \right)}}} \\{{P_{apr}\left( S_{5} \right)} = {{P\left( S_{- 10}^{*} \right)} \cdot {P_{apr}\left( S_{01}^{*} \right)} \cdot {P\left( S_{11}^{*} \right)}}} \\{{P_{apr}\left( S_{6} \right)} = {{P\left( S_{- 11}^{*} \right)} \cdot {P_{apr}\left( S_{01}^{*} \right)} \cdot {P\left( S_{10}^{*} \right)}}} \\{{P_{apr}\left( S_{7} \right)} = {{P\left( S_{- 11}^{*} \right)} \cdot {P_{apr}\left( S_{01}^{*} \right)} \cdot {P\left( S_{11}^{*} \right)}}}\end{matrix} \right. & (7)\end{matrix}$

In expressions (6)-(7), P_(apr) (S_(j)) is a prior probability(transmission probability) of the information signal S_(j) with thenumber j in the target sub-channel being transmitted. Prior probabilityP_(apr) (S*_(ij)) depends on the statistics of the data generationsource, and in practical terms it is assumed to be equal to ½.Probability P (S*_(ij)) is the posterior probability of the receivesignal S*_(ij), which is different from the prior probability P_(apr)(S*_(ij)), and can be estimated at the receive side with highreliability, so P (S*_(ij))≈P (S*_(ij)/y(t)). This is the best estimateof P (S*_(ij)) in the white Gaussian noise channel. And based on thisassumption, the expressions (6) and (7) can be rewritten as

$\begin{matrix}\left\{ \begin{matrix}{{P_{apr}\left( S_{0} \right)} = {{P\left( {S_{- 10}^{*}/{y(t)}} \right)} \cdot {P_{apr}\left( S_{00}^{*} \right)} \cdot {P\left( {S_{10}^{*}/{y(t)}} \right)}}} \\{{P_{apr}\left( S_{1} \right)} = {{P\left( {S_{- 10}^{*}/{y(t)}} \right)} \cdot {P_{apr}\left( S_{00}^{*} \right)} \cdot {P\left( {S_{11}^{*}/{y(t)}} \right)}}} \\{{P_{apr}\left( S_{2} \right)} = {{P\left( {S_{- 11}^{*}/{y(t)}} \right)} \cdot {P_{apr}\left( S_{00}^{*} \right)} \cdot {P\left( {S_{10}^{*}/{y(t)}} \right)}}} \\{{P_{apr}\left( S_{3} \right)} = {{P\left( {S_{- 11}^{*}/{y(t)}} \right)} \cdot {P_{apr}\left( S_{00}^{*} \right)} \cdot {P\left( {S_{11}^{*}/{y(t)}} \right)}}}\end{matrix} \right. & (8)\end{matrix}$ $\begin{matrix}\left\{ \begin{matrix}{{P_{apr}\left( S_{4} \right)} = {{P\left( {S_{- 10}^{*}/{y(t)}} \right)} \cdot {P_{apr}\left( S_{01}^{*} \right)} \cdot {P\left( {S_{10}^{*}/{y(t)}} \right)}}} \\{{P_{apr}\left( S_{5} \right)} = {{P\left( {S_{- 10}^{*}/{y(t)}} \right)} \cdot {P_{apr}\left( S_{01}^{*} \right)} \cdot {P\left( {S_{11}^{*}/{y(t)}} \right)}}} \\{{P_{apr}\left( S_{6} \right)} = {{P\left( {S_{- 11}^{*}/{y(t)}} \right)} \cdot {P_{apr}\left( S_{01}^{*} \right)} \cdot {P\left( {S_{10}^{*}/{y(t)}} \right)}}} \\{{P_{apr}\left( S_{7} \right)} = {{P\left( {S_{- 11}^{*}/{y(t)}} \right)} \cdot {P_{apr}\left( S_{01}^{*} \right)} \cdot {P\left( {S_{11}^{*}/{y(t)}} \right)}}}\end{matrix} \right. & (9)\end{matrix}$or when a different relationship exists between the information signalS*_(ij) and the transmission information signal D_(i) (see expression(1)), a substitution of P (S*_(ij))=P (D_(i)=i/y(t)) is possible inexpression (6) and (7), and expressions (6) and (7) can be expressed bythe following expressions. Here P (S*_(ij)) is a probability of the i-thsub-channel Di becoming j

$\begin{matrix}\left\{ \begin{matrix}{{P_{apr}\left( S_{0} \right)} = {{P\left( {D_{- 1} = {{+ 1}/{y(t)}}} \right)} \cdot {P_{apr}\left( S_{00}^{*} \right)} \cdot {P\left( {S_{1} = {{+ 1}/{y(t)}}} \right)}}} \\{{P_{apr}\left( S_{1} \right)} = {{P\left( {D_{- 1} = {{+ 1}/{y(t)}}} \right)} \cdot {P_{apr}\left( S_{00}^{*} \right)} \cdot {P\left( {D_{1} = {{- 1}/{y(t)}}} \right)}}} \\{{P_{apr}\left( S_{2} \right)} = {{P\left( {D_{- 1} = {{- 1}/{y(t)}}} \right)} \cdot {P_{apr}\left( S_{00}^{*} \right)} \cdot {P\left( {S_{1} = {{+ 1}/{y(t)}}} \right)}}} \\{{P_{apr}\left( S_{3} \right)} = {{P\left( {D_{- 1} = {{- 1}/{y(t)}}} \right)} \cdot {P_{apr}\left( S_{00}^{*} \right)} \cdot {P\left( {D_{1} = {{- 1}/{y(t)}}} \right)}}}\end{matrix} \right. & (10)\end{matrix}\begin{matrix}\left\{ \begin{matrix}{{P_{apr}\left( S_{4} \right)} = {{P\left( {D_{- 1} = {{+ 1}/{y(t)}}} \right)} \cdot {P_{apr}\left( S_{01}^{*} \right)} \cdot {P\left( {D_{1} = {{+ 1}/{y(t)}}} \right)}}} \\{{P_{apr}\left( S_{5} \right)} = {{P\left( {D_{- 1} = {{+ 1}/{y(t)}}} \right)} \cdot {P_{apr}\left( S_{01}^{*} \right)} \cdot {P\left( {D_{1} = {{- 1}/{y(t)}}} \right)}}} \\{{P_{apr}\left( S_{6} \right)} = {{P\left( {D_{- 1} = {{- 1}/{y(t)}}} \right)} \cdot {P_{apr}\left( S_{01}^{*} \right)} \cdot {P\left( {D_{1} = {{+ 1}/{y(t)}}} \right)}}} \\{{P_{apr}\left( S_{7} \right)} = {{P\left( {D_{- 1} = {{- 1}/{y(t)}}} \right)} \cdot {P_{apr}\left( S_{01}^{*} \right)} \cdot {P\left( {D_{1} = {{- 1}/{y(t)}}} \right)}}}\end{matrix} \right. & (11)\end{matrix}$

In the expressions (10) and (11) the prior probability P_(apr)(S_(j))(j=0, 1, 2, . . . 7) of the receive signal S_(j) in the targetsub-channel is expressed by the cross-channel product of the priortransmission probability P_(apr) (S*_(ij)) of the information signalS*_(ij), and the posterior probability of the information symbol D_(i)received by the lower and upper adjacent channels being +1 or −1.

In the turbo receiver (maximum likely receiver) of the presentinvention, the sign of the receive information symbol D₀ of the targetsub-channel is determined as follows. That is, the probability of thereceive information symbol D₀ of the target sub-channel (number 0) being+1, which is P (D₀=+1/y(t)) and the probability of D₀ being −1, which isP (D₀=−1/y(t)) are determined respectively, and the sign of the receiveinformation symbol D₀ is determined by comparing the values thereof, orcomparing the difference of the logarithm thereof and the thresholdvalue.

The posterior probability P (D₀=j/y(t)) of the receive informationsymbol D₀ of the target sub-channel being j can be acquired as theposterior probability of the signals of which D₀ is j being received.Therefore the posterior probability P (D₀=+1/y(t)) is a probability ofthe receive information signal D₀ of the target sub-channel becoming “0”(=+1) can be determined as follows. That is, the signal to transmit theinformation symbol of “0” (=+1) in the target sub-channel is S₀-S₃according to the expressions (1) and (2), so the posterior probability P(D₀=+1/y(t)) of the receive information symbol D₀ of the targetsub-channel becoming “0” (=+1) becomes the sum of the posteriorprobability to receive the signals S₀-S₃, which can be determined by theexpression (12a). In the same way, the posterior probability P(D₀=−1/y(t)) of the receive information symbol D₀ of the targetsub-channel becoming “0” (=−1) can be determined by the expression

$\left\{ \begin{matrix}{{P\left( {D_{0} = {{+ 1}/{y(t)}}} \right)} = {k \cdot \left\lbrack {{P\left( {S_{0}/{y(t)}} \right)} + {P\left( {S_{1}/{y(t)}} \right)} + {P\left( {S_{2}/{y(t)}} \right)} + {P\left( {S_{3}/{y(t)}} \right\rbrack}} \right.}} & \left( {12a} \right) \\{{P\left( {D_{0} = {{- 1}/{y(t)}}} \right)} = {k \cdot \left\lbrack {{P\left( {S_{4}/{y(t)}} \right)} + {P\left( {S_{5}/{y(t)}} \right)} + {P\left( {S_{6}/{y(t)}} \right)} + {P\left( {S_{7}/{y(t)}} \right)}} \right\rbrack}} & \left( {12b} \right)\end{matrix} \right.$If the expression (5) is applied to (12a) (where k₀=1), the expression(13) is established,P(D ₀=+1/y(t))=k·[P _(apr)(S ₀)·P(y(t)/S ₀)+P _(apr)(S ₁)·P(y(t)/S₁)+k·[P _(apr)(S ₂)·P(y(t)/S ₂)+P _(apr)(S ₃)·P(y(t)/S ₃)]  (13)and if the expression (5) is applied to (12b) (where k₀=1), theexpression (14) is established.P(D ₀=−1/y(t))=k·[P _(apr)(S ₄)·P(y(t)/S ₄)+P _(apr)(S ₅)·P(y(t)/S₅)+k·[P _(apr)(S ₆)·P(y(t)/S ₆)+P _(apr)(S ₇)·P(y(t)/S ₇)]  (14)If the expressions (10) and (11) are substituted for the expressions(13) and (14) and y(t) of P (D_(i)=±1/y(t)) is omitted forsimplification (that is P (D_(i)=±1/y(t))=P (D_(i)=±1)), then theexpressions (15) and (16) are acquired.

$\begin{matrix}{{P\left( {D_{0} = {{+ 1}/{y(t)}}} \right)} = {k \cdot \begin{bmatrix}{{{P\left( {D_{- 1} = {+ 1}} \right)} \cdot {P_{apr}\left( S_{00}^{*} \right)} \cdot {P\left( {D_{1} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{0}} \right)}} +} \\{{{P\left( {D_{- 1} = {+ 1}} \right)} \cdot {P_{apr}\left( S_{00}^{*} \right)} \cdot {P\left( {D_{1} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{1}} \right)}} +} \\{{{P\left( {D_{- 1} = {- 1}} \right)} \cdot {P_{apr}\left( S_{00}^{*} \right)} \cdot {P\left( {D_{1} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{2}} \right)}} +} \\{{P\left( {D_{- 1} = {- 1}} \right)} \cdot {P_{apr}\left( S_{00}^{*} \right)} \cdot {P\left( {D_{1} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{3}} \right)}}\end{bmatrix}}} & (15)\end{matrix}$

$\begin{matrix}{{P\left( {D_{0} = {{- 1}/{y(t)}}} \right)} = {k \cdot \begin{bmatrix}{{{P\left( {D_{- 1} = {+ 1}} \right)} \cdot {P_{apr}\left( S_{01}^{*} \right)} \cdot {P\left( {D_{1} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{4}} \right)}} +} \\{{{P\left( {D_{- 1} = {+ 1}} \right)} \cdot {P_{apr}\left( S_{01}^{*} \right)} \cdot {P\left( {D_{1} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{5}} \right)}} +} \\{{{P\left( {D_{- 1} = {- 1}} \right)} \cdot {P_{apr}\left( S_{01}^{*} \right)} \cdot {P\left( {D_{1} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{6}} \right)}} +} \\{{P\left( {D_{- 1} = {- 1}} \right)} \cdot {P_{apr}\left( S_{01}^{*} \right)} \cdot {P\left( {D_{1} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{7}} \right)}}\end{bmatrix}}} & (16)\end{matrix}$Then the expression (15) is further transformed, and the expressions(17a) and (17b) are acquired.P(D ₀=+1/y(t))=k·P _(apr)(S ₀₀ ^(*))·[P(D ⁻¹=+1)·P(D ₁=+1)·P(y(t)/S₀)+P(D ⁻¹=+1)·P(D ₁=−1)·P(y(t)/S ₁)]+k·P _(apr)(S ₀₀ ^(*))·[P(D⁻¹=−1)·P(D ₁=+1)·P(y(t)/S ₂)+P(D ⁻¹=−1)·P(D ₁=−1)·P(y(t)/S ₃)]  (17a)P(D ₀=+1/y(t))=k·P _(apr)(S ₀₀ ^(*))·[P(D ⁻¹=+1)·{P(D ₁=+1)·P(y(t)/S₀)+P(D ₁=−1)·P(y(t)/S ₁)}]+k·P _(apr)(S ₀₀ ^(*))·[P(D ⁻¹=−1)·{P(D₁=+1)·P(y(t)/S ₂)+P(D ₁=−1)·P(y(t)/S ₃)}]  (17b)In the same way, the expression (16) is transformed, and the expressions(18a) and (18b) are acquired.P(D ₀=−1/y(t))=k·P _(apr)(S ₀₁ ^(*))·[P(D ⁻¹=+1)·P(D ₁=+1)·P(y(t)/S₄)+P(D ⁻¹=+1)·P(D ₁=−1)·P(y(t)/S ₅)]+k·P _(apr)(S ₀₀ ^(*))·[P(D⁻¹=−1)·P(D ₁=+1)·P(y(t)/S ₆)+P(D ⁻¹=−1)·P(D ₁=−1)·P(y(t)/S ₇)]  (18a)P(D ₀=−1/y(t))=k·P _(apr)(S ₀₁ ^(*))·[P(D ⁻¹=+1)·{P(D ₁=+1)·P(y(t)/S₄)+P(D ₁=−1)·P(y(t)/S ₅)}]+k·P _(apr)(S ₀₁ ^(*))·[P(D ⁻¹=−1)·{P(D₁=+1)·P(y(t)/S ₆)+P(D ₁=−1)·P(y(t)/S ₇)}]  (18b)

If the posterior probabilities P (D₀=+1/y(t)) and P (D₀=−1/y(t)) for thereceive information symbol D₀ of the target sub-channel becoming “0”(=+1) and “1” (=−1) are determined as above, the values are compared orthe difference of the logarithm thereof and the threshold value arecompared so as to determined the sine (+1 or −1) of the receiveinformation symbol.

-   -   Decision by comparing values

Whether the information symbol D₀ of the target sub-channel is +1 or −1is decided by computing P (D₀=+1/y(t)) and P (D₀=−1/y(t)) first, then byusing the expressions (19a) and (19b),

$\begin{matrix}{\frac{P\left( {D_{0} = {{+ 1}/{y(t)}}} \right)}{P\left( {D_{0} = {{- 1}/{y(t)}}} \right)} > 1} & \left( {19a} \right) \\{\frac{P\left( {D_{0} = {{+ 1}/{y(t)}}} \right)}{P\left( {D_{0} = {{- 1}/{y(t)}}} \right)} < 1} & \left( {19b} \right)\end{matrix}$and if (19a), then it is decided as D₀=+1, and if (19b), then it isdecided as D₀=−1.

-   -   Decision by difference of logarithm

Whether the information symbol D₀ of the target sub-channel is +1 or −1is decided by computing ln P(D₀=+1/y(t))−ln P(D₀=−1/y(t)) (ln is alogarithm with an e base), then deciding the negative/positive of theresult. Ifln P(D ₀=+1/y(t))−ln P(D ₀=−1/y(t))>0  (19c),then it is decided as D₀=+1, and ifln P(D ₀=+1/y(t))−ln P(D ₀=−1/y(t))<0  (19d),then it is decided as D₀=−1.

Since the transmission symbol D₀ is statistically independent (nocorrelation) and is an equally distributed probability variable, thefollowing expression is established.

$\begin{matrix}\left\{ \begin{matrix}{{P_{apr}\left( S_{- 10}^{*} \right)} = {{P_{apr}\left( S_{00}^{*} \right)} = {{P_{apr}\left( S_{+ 10}^{*} \right)} = {1/2}}}} \\{{P_{apr}\left( S_{- 11}^{*} \right)} = {{P_{apr}\left( S_{01}^{*} \right)} = {{P_{apr}\left( S_{+ 11}^{*} \right)} = {1/2}}}}\end{matrix} \right. & (20)\end{matrix}$As expression (20) shows, the common multiplier in the expressions (17b)and (18b) does not affect the decision rule, so the expressions (17b)and (18b) become the expressions (21) and (22).P(D ₀=+1/y(t))=P(D ⁻¹=+1)·{P(D ₁=+1)·P(y(t)/S ₀)+P(D ₁=−1)·P(y(t)/S₁)}+P(D ⁻¹=−1)·{P(D ₁=+1)·P(y(t)/S ₂)+P(D ₁=−1)·P(y(t)/S ₃)}  (21)P(D ₀=−1/y(t))=P(D ⁻¹=+1)·{P(D ₁=+1)·P(y(t)/S ₄)+P(D ₁=−1)·P(y(t)/S₅)}+P(D ⁻¹=−1)·{P(D ₁=+1)·P(y(t)/S ₆)+P(D ₁=−1)·P(y(t)/S ₇)}  (22)If the expressions (21) and (22) are transformed considering thealgebraic sameness of the following expression,

$\begin{matrix}{{\ln\left( {{\mathbb{e}}^{X} + {\mathbb{e}}^{Y}} \right)} = {\frac{X + Y}{2} + {\ln\mspace{14mu} 2} + {\ln\mspace{14mu}{\cosh\left( \frac{X - Y}{2} \right)}}}} & (a)\end{matrix}$then the following expressions (23) and (24) are established.

$\begin{matrix}{{\ln\mspace{14mu}{P\left( {D_{0} = {{+ 1}/{y(t)}}} \right)}} = {{{{1/2} \cdot \ln}\mspace{14mu}{P\left( {D_{- 1} = {+ 1}} \right)}} + {{1/2} \cdot \ln \cdot \left\{ {{{P\left( {D_{1} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{0}} \right)}} + {{{P\left( {D_{1} = {- 1}} \right)} \cdot P}\left( {{y(t)}/S_{1}} \right)}} \right\}} + {{{1/2} \cdot \ln}\mspace{14mu}{P\left( {D_{- 1} = {- 1}} \right)}} + {{{1/2} \cdot \ln}\left\{ {{{P\left( {D_{1} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{2}} \right)}} + {{P\left( {D_{1} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{3}} \right)}}} \right\}} + {\ln\mspace{14mu} 2} + {\ln\mspace{14mu}\cosh\begin{Bmatrix}\begin{matrix}{{{{1/2} \cdot \ln}\mspace{14mu}{P\left( {D_{- 1} = {+ 1}} \right)}} + {{{1/2} \cdot \ln}\left\{ {{P\left( {D_{1} = {+ 1}} \right)} \cdot} \right.}} \\{\left. {{P\left( {{y(t)}/S_{0}} \right)} + {{P\left( {D_{1} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{1}} \right)}}} \right\} -}\end{matrix} \\\begin{matrix}{{{{1/2} \cdot \ln}\mspace{14mu}{P\left( {D_{- 1} = {- 1}} \right)}} + {{{1/2} \cdot \ln}\left\{ {{P\left( {D_{1} = {+ 1}} \right)} \cdot} \right.}} \\\left. {{P\left( {{y(t)}/S_{2}} \right)} + {{P\left( {D_{1} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{3}} \right)}}} \right\}\end{matrix}\end{Bmatrix}}}} & (23) \\{{\ln\mspace{14mu}{P\left( {D_{0} = {{- 1}/{y(t)}}} \right)}} = {{{{1/2} \cdot \ln}\mspace{14mu}{P\left( {D_{- 1} = {+ 1}} \right)}} + {{1/2} \cdot \ln \cdot \left\{ {{{P\left( {D_{1} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{4}} \right)}} + {{{P\left( {D_{1} = {- 1}} \right)} \cdot P}\left( {{y(t)}/S_{5}} \right)}} \right\}} + {{{1/2} \cdot \ln}\mspace{14mu}{P\left( {D_{- 1} = {- 1}} \right)}} + {{{1/2} \cdot \ln}\left\{ {{{P\left( {D_{1} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{6}} \right)}} + {{P\left( {D_{1} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{7}} \right)}}} \right\}} + {\ln\mspace{14mu} 2} + {\ln\mspace{14mu}\cosh\begin{Bmatrix}\begin{matrix}{{{{1/2} \cdot \ln}\mspace{14mu}{P\left( {D_{- 1} = {+ 1}} \right)}} + {{{1/2} \cdot \ln}\left\{ {{P\left( {D_{1} = {+ 1}} \right)} \cdot} \right.}} \\{\left. {{P\left( {{y(t)}/S_{4}} \right)} + {{P\left( {D_{1} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{5}} \right)}}} \right\} -}\end{matrix} \\\begin{matrix}{{{{1/2} \cdot \ln}\mspace{14mu}{P\left( {D_{- 1} = {- 1}} \right)}} + {{{1/2} \cdot \ln}\left\{ {{P\left( {D_{1} = {+ 1}} \right)} \cdot} \right.}} \\\left. {{P\left( {{y(t)}/S_{6}} \right)} + {{P\left( {D_{1} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{7}} \right)}}} \right\}\end{matrix}\end{Bmatrix}}}} & (24) \\{{\ln\mspace{14mu}{P\left( {D_{0} = {{+ 1}/{y(t)}}} \right)}} = {\frac{A + B}{2} + {\ln\mspace{14mu} 2} + {\ln\mspace{14mu}{\cosh\left( \frac{A - B}{2} \right)}}}} & (25) \\{{\ln\mspace{14mu}{P\left( {D_{0} = {{- 1}/{y(t)}}} \right)}} = {\frac{C + D}{2} + {\ln\mspace{14mu} 2} + {\ln\mspace{14mu}{\cosh\left( \frac{C - D}{2} \right)}}}} & (26)\end{matrix}$Here if the expressions (25) and (26) are used, then A, B, C and Dbecome as follows.A=ln P(D ⁻¹=+1)+ln {P(D ₁=+1)·P(y(t)/S₀)+P(D ₁=−1)·P(y(t)/S ₁)}B=ln P(D ⁻¹=−1)+ln {P(D ₁=+1)·P(y(t)/S ₂)+P(D ₁=−1)·P(y(t)/S ₃)}C=ln P(D ⁻¹=+1)+ln {P(D ₁=+1)·P(y(t)/S₄)+P(D ₁=−1)·P(y(t)/S ₅)}D=ln P(D ⁻¹=−1)+ln {P(D ₁=+1)·P(y(t)/S ₆)+P(D ₁=−1)·P(y(t)/S ₇)}

If the expressions (25) and (26) are applied to the left side member ofthe expressions (19c) and (19d), the new decision expression becomes asfollows.

$\begin{matrix}{{\ln\mspace{14mu} D_{0}} = {{\frac{A + B}{2} - \frac{C + D}{2} + {\ln\mspace{14mu}{\cosh\left( \frac{A - B}{2} \right)}} - {\ln\mspace{14mu}{\cosh\left( \frac{C - D}{2} \right)}}} > {/{< 0}}}} & (27)\end{matrix}$By considering the relationship of

${P\left( {{y(t)}/S_{j}} \right)} = {\exp\left\{ {{- \frac{1}{N_{0}}}{\int_{0}^{T}{\left\lbrack {{y(t)} - S_{j}} \right\rbrack^{2}{\mathbb{d}t}}}} \right\}}$acquired by the expression (5) and the expression (4), each termconstituting the new decision expression (27) can be rewritten asfollows.Here ln D_(i)=ln P (D_(i)=+1)−ln P (D_(i)=−1).

$\begin{matrix}{{\left( {A + B} \right) - \left( {C + D} \right)} = {{\frac{2}{N_{0}}\left\lbrack {{\int_{0}^{T}{{{y(t)} \cdot {S_{0}(t)}}{\mathbb{d}t}}} + {\int_{0}^{T}{{{y(t)} \cdot {S_{1}(t)}}{\mathbb{d}t}}} + {\int_{0}^{T}{{{y(t)} \cdot {S_{2}(t)}}{\mathbb{d}t}}} + {\int_{0}^{T}{{{y(t)} \cdot {S_{3}(t)}}{\mathbb{d}t}}}} \right\rbrack} + {\ln\mspace{14mu}\cosh\left\{ {{1/2} \cdot \left\{ {{\ln\mspace{14mu} D_{1}} + {\frac{2}{N_{0}}\left\lbrack {{\int_{0}^{T}{{{y(t)} \cdot {S_{0}(t)}}{\mathbb{d}t}}} - {\int_{0}^{T}{{{y(t)} \cdot {S_{1}(t)}}{\mathbb{d}t}}}} \right\rbrack} - \frac{E_{0} - E_{1}}{N_{0}}} \right\}} \right\}} - {\ln\mspace{14mu}\cosh\left\{ {{1/2} \cdot \left\{ {{\ln\mspace{14mu} D_{1}} + {\frac{2}{N_{0}}\left\lbrack {{\int_{0}^{T}{{{y(t)} \cdot {S_{0}(t)}}{\mathbb{d}t}}} - {\int_{0}^{T}{{{y(t)} \cdot {S_{1}(t)}}{\mathbb{d}t}}}} \right\rbrack} + \frac{E_{0} - E_{1}}{N_{0}}} \right\}} \right\}} + {\ln\mspace{14mu}\cosh\left\{ {{1/2} \cdot \left\{ {{\ln\mspace{14mu} D_{1}} + {\frac{2}{N_{0}}\left\lbrack {{\int_{0}^{T}{{{y(t)} \cdot {S_{2}(t)}}{\mathbb{d}t}}} - {\int_{0}^{T}{{{y(t)} \cdot {S_{3}(t)}}{\mathbb{d}t}}}} \right\rbrack} - \frac{E_{2} - E_{3}}{N_{0}}} \right\}} \right\}} - {\ln\mspace{14mu}\cosh\left\{ {{1/2} \cdot \left\{ {{\ln\mspace{14mu} D_{1}} + {\frac{2}{N_{0}}\left\lbrack {{\int_{0}^{T}{{{y(t)} \cdot {S_{2}(t)}}{\mathbb{d}t}}} - {\int_{0}^{T}{{{y(t)} \cdot {S_{3}(t)}}{\mathbb{d}t}}}} \right\rbrack} + \frac{E_{2} - E_{3}}{N_{0}}} \right\}} \right\}}}} & (28)\end{matrix}$In the above description, ln D_(i)=ln P (D_(i)=+1/y(t))−ln P(D_(i)=−1/y(t)) is the logarithmic difference of the posteriorprobabilities of the signal D_(i) transmitted in the i-th sub-channelbeing +1 and −1 (soft decision value of the i-th sub-channel). It isassumed that the energy of the signal S_(j)(t) is E_(j), and

E_(j) = ∫₀^(T)S_(j)²(t)𝕕t.(A−B), (C−D) of the expression (27) becomes as follows.

$\begin{matrix}{\left( {A - B} \right) = {{\ln\mspace{14mu} D_{- 1}} + {{1/2} \cdot \left\{ {{\frac{2}{N_{0}}\left\lbrack {{\int_{0}^{T}{{{y(t)} \cdot {S_{0}(t)}}{\mathbb{d}t}}} + {\int_{0}^{T}{{{y(t)} \cdot {S_{1}(t)}}{\mathbb{d}t}}} - {\int_{0}^{T}{{{y(t)} \cdot {S_{2}(t)}}{\mathbb{d}t}}} - {\int_{0}^{T}{{{y(t)} \cdot {S_{3}(t)}}{\mathbb{d}t}}}} \right\rbrack} - \frac{\Delta\; E_{\Sigma}}{N_{0}}} \right\}} + {\ln\mspace{14mu}\cosh\left\{ {{1/2} \cdot \left\{ {{\ln\mspace{14mu} D_{1}} + {\frac{2}{N_{0}}\left\lbrack {{\int_{0}^{T}{{{y(t)} \cdot {S_{0}(t)}}{\mathbb{d}t}}} - {\int_{0}^{T}{{{y(t)} \cdot {S_{1}(t)}}{\mathbb{d}t}}}} \right\rbrack} - \frac{E_{0} - E_{1}}{N_{0}}} \right\}} \right\}} - {\ln\mspace{14mu}\cosh\left\{ {{1/2} \cdot \left\{ {{\ln\mspace{14mu} D_{1}} + {\frac{2}{N_{0}}\left\lbrack {{\int_{0}^{T}{{{y(t)} \cdot {S_{2}(t)}}{\mathbb{d}t}}} - {\int_{0}^{T}{{{y(t)} \cdot {S_{3}(t)}}{\mathbb{d}t}}}} \right\rbrack} + \frac{E_{2} - E_{3}}{N_{0}}} \right\}} \right\}}}} & (29) \\{\left( {C - D} \right) = {{\ln\mspace{14mu} D_{- 1}} + {{1/2} \cdot \left\{ {{\frac{2}{N_{0}}\left\lbrack {{\int_{0}^{T}{{{y(t)} \cdot {S_{0}(t)}}{\mathbb{d}t}}} + {\int_{0}^{T}{{{y(t)} \cdot {S_{1}(t)}}{\mathbb{d}t}}} - {\int_{0}^{T}{{{y(t)} \cdot {S_{2}(t)}}{\mathbb{d}t}}} - {\int_{0}^{T}{{{y(t)} \cdot {S_{3}(t)}}{\mathbb{d}t}}}} \right\rbrack} + \frac{\Delta\; E_{\Sigma}}{N_{0}}} \right\}} + {\ln\mspace{14mu}\cosh\left\{ {{1/2} \cdot \left\{ {{\ln\mspace{14mu} D_{1}} + {\frac{2}{N_{0}}\left\lbrack {{\int_{0}^{T}{{{y(t)} \cdot {S_{0}(t)}}{\mathbb{d}t}}} - {\int_{0}^{T}{{{y(t)} \cdot {S_{1}(t)}}{\mathbb{d}t}}}} \right\rbrack} + \frac{E_{0} - E_{1}}{N_{0}}} \right\}} \right\}} - {\ln\mspace{14mu}\cosh\left\{ {{1/2} \cdot \left\{ {{\ln\mspace{14mu} D_{1}} + {\frac{2}{N_{0}}\left\lbrack {{\int_{0}^{T}{{{y(t)} \cdot {S_{2}(t)}}{\mathbb{d}t}}} - {\int_{0}^{T}{{{y(t)} \cdot {S_{3}(t)}}{\mathbb{d}t}}}} \right\rbrack} + \frac{E_{2} - E_{3}}{N_{0}}} \right\}} \right\}}}} & (30)\end{matrix}$where

$\begin{matrix}{{\Delta\; E_{\Sigma}} = \frac{\left( {E_{0} + E_{1}} \right) - \left( {E_{2} + E_{3}} \right)}{N_{0}}} & (31)\end{matrix}$The expressions (27)-(30) define the optimum receiver structure ofbinary signals involving ICI. As the expressions (27)-(30) show, thedecision information of the adjacent channels is used to decide the signof the transmission information symbol D of a sub-channel. In thedecision rule of the expressions (27)-(30), ln D⁻¹ and ln D₊₁ indicatethe logarithmic difference of the posterior probability of theinformation symbol in the lower sub-channel (ch−1) and the uppersub-channel (ch+1) becoming +1 and the posterior probability of thatbecoming −1. All calculations are in series, so when processing the dataof the target sub-channel, the latest posterior probability from theadjacent channels can be used by repeat calculation.

As described above, the algorithm is created such that InD₀, which isthe soft decision target value, is computed by the expressions(27)-(30), then “0” or “1” of the receive symbol of the targetsub-channel is decided depending on the positive/negative of the softdecision target value InD₀.

(C) Configuration of Receiver

FIG. 5 is a block diagram depicting a receiver of a three sub-channelmodel, that is, a receiver based on the maximum posterior probabilityusing ICI (called a turbo receiver), and shows the configuration of onlythe receive unit of the target sub-channel, but the receive units of theother sub-channels also have the same configuration. This receive unitalso has a configuration to execute the above mentioned algorithm.

The receiver 50 of the target sub-channel further comprises acorrelation unit (can be a match fill) 51, another channel decisionresult operating unit 52, first and second non-linear units 53 and 54,and symbol decision unit 55.

The multiplier 51 a and integrator 51 b of the correlation unit 51 is aunit for computing

$\frac{2}{N_{0}}{\int_{o}^{T}{{{y(t)} \cdot {S_{0}(t)}}{\mathbb{d}t}}}$of the decision expressions (28)-(30), the multiplier 51 c andintegrator 51 d are units for computing

${\frac{2}{N_{0}}{\int_{o}^{T}{{{y(t)} \cdot {S_{1}(t)}}\;{\mathbb{d}t}}}},$the multiplier 51 e and integrator 51 f are units for computing

${\frac{2}{N_{0}}{\int_{o}^{T}{{{y(t)} \cdot {S_{2}(t)}}{\mathbb{d}t}}}},$and the multiplier 51 g and integrator 51 h are units for computing

$\frac{2}{N_{0}}{\int_{o}^{T}{{{y(t)} \cdot {S_{3}(t)}}{{\mathbb{d}t}.}}}$The addition unit 51 i adds the integration output of the integrators 51b and 51 d, subtractor 51 j subtracts the integration outputs of theintegrators 51 b and 51 d, the addition unit 51 k adds the integrationoutputs of the integrators 51 f and 51 h, and the subtractor 51 msubtracts the integration outputs of the integrators 51 f and 51 h. Theaddition unit 51 n adds the outputs of the addition units 51 i and 51 k,and outputs the first term of the right side member of the expression(28), that is

$\left. {{\frac{2}{N_{0}}{\int_{o}^{T}{{{y(t)} \cdot {S_{0}(t)}}{\mathbb{d}t}}}} + {\frac{2}{N_{0}}{\int_{0}^{T}{{y(t)}{S_{1}(t)}{\mathbb{d}t}}}} + {\frac{2}{N_{0}}{\int_{0}^{T}{{y(t)}{S_{2}(t)}{\mathbb{d}t}}}} + {\frac{2}{N_{0}}{\int_{0}^{T}{{y(t)}{S_{3}(t)}}}}} \right){\mathbb{d}t}$The subtraction unit 51 _(p) subtracts the outputs of the addition units51 i and 51 k, and outputs

$\left. {{\frac{2}{N_{0}}{\int_{o}^{T}{{{y(t)} \cdot {S_{0}(t)}}{\mathbb{d}t}}}} + {\frac{2}{N_{0}}{\int_{0}^{T}{{y(t)}{S_{1}(t)}{\mathbb{d}t}}}} - {\frac{2}{N_{0}}{\int_{0}^{T}{{y(t)}{S_{2}(t)}{\mathbb{d}t}}}} - {\frac{2}{N_{0}}{\int_{0}^{T}{{y(t)}{S_{3}(t)}}}}} \right){\mathbb{d}t}$The division units 51 q and 51 r divide the input signal ½, and outputthe result.

The other channel decision result operating unit 52 comprises the adders52 a-52 c, which compute the following respectively.

$\left. {{{\ln\mspace{11mu} D_{+ 1}} + {\frac{2}{N_{0}}{\int_{o}^{T}{{{y(t)} \cdot {S_{0}(t)}}{\mathbb{d}t}}}} - {\frac{2}{N_{0}}{\int_{0}^{T}{{y(t)}{S_{1}(t)}{\mathbb{d}t}}}}},{{\ln\mspace{11mu} D_{+ 1}} + {\frac{2}{N_{0}}{\int_{o}^{T}{{{y(t)} \cdot {S_{2}(t)}}{\mathbb{d}t}}}} - {\frac{2}{N_{0}}{\int_{0}^{T}{{y(t)}{S_{3}(t)}{\mathbb{d}t}}}}},{{\ln\mspace{11mu} D_{- 1}} + {\frac{1}{N_{0}}{\int_{o}^{T}{{{y(t)} \cdot {S_{0}(t)}}{\mathbb{d}t}}}} + {\frac{1}{N_{0}}{\int_{0}^{T}{{y(t)}{S_{1}(t)}{\mathbb{d}t}}}} - {\frac{1}{N_{0}}{\int_{0}^{T}{{{y(t)} \cdot {S_{2}(t)}}{\mathbb{d}t}}}} - {\frac{1}{N_{0}}{\int_{0}^{T}{{y(t)}{S_{3}(t)}}}}}} \right){\mathbb{d}t}$

The first non-linear unit 53 is a unit for computing ln cosh of thesecond-fifth terms of the right side member of the expression (28), andcomprises the first and second non-linear sections 53 a and 53 b. Theaddition units 71 a and 71 b of the first non-linear section 53 acompute the content of { } of the second and third terms of the rightside member of the expression (28) respectively. Here the(E₀−E₁)/N₀=ΔE₁. ln cosh computing units 71 c and 71 d compute the secondand third terms of the right side member of the expression (28)respectively, and the subtractor 71 e subtracts the computing result ofthe ln cosh computing unit 71 d from the computing result of the ln coshcomputing unit 71 c.

The addition units 71 a′ and 71 b′ of the second non-linear unit 53 bcompute the content of { } of the fourth and fifth terms of the rightside member of the expression (28) respectively. Here the (E₂−E₃)/N₀=ΔE₂ln cosh computing units 71 c′ and 71 d′ compute the fourth and fifthterms of the right side member of the expression (28) respectively, andthe subtractor 71 e′ subtracts the computing result of the in coshcomputing unit 71 d′ from the computing result of the in cosh computingunit 71 c′, and outputs the result.

The addition unit 53 c synthesizes the outputs of the adders 71 e and 71e′ and the division unit 53 d divides the synthesized signal by ½, andoutputs the computing results of the second-fifth terms of theexpression (28).

The second non-linear unit 54 is a unit for computing the first-thirdterms of the right side member of the expressions (29) and (30). Theaddition units 54 a and 54 b compute the first term of the right sidemember of the expressions (29) and (30) respectively, the addition units54 c and 54 d compute the second term and third term of the right sidemember of the expressions (29) and (30) respectively, the addition units54 e and 54 f compute the right side member of the expressions (29) and(30) respectively, ln cosh computing units 54 g and 54 h compute ln cosh

$\frac{A - B}{2}\mspace{14mu}{and}\mspace{14mu}\ln\mspace{11mu}\cosh\;\frac{C - D}{2}$respectively, and the subtraction unit 54 i computes the differencebetween the outputs of the ln cosh computing units 54 g and 54 h, andoutputs

${\ln\mspace{11mu}\cosh\;\frac{A - B}{2}} - {\ln\mspace{11mu}\cosh\;{\frac{C - D}{2}.}}$

The adder 55 a of the symbol decision unit 55 adds the output signal ofthe division unit 51 r of the correlation unit 51 and the output signalof the non-linear unit 53, and outputs

${\frac{A - B}{2} - \frac{C - D}{2}},$and the addition unit 55 b generates the InD₀ (soft decision targetvalue) of the expression (27). The decision unit 55 c decides whetherInD₀ is positive or negative, and decides that the receive symbol is “0” if positive, and that it is −1′ if negative. The symbol decision unit55 feeds back the computing result (soft decision target value) InD₀ ofthe expression (27) to the other channel decision result operating unitsof the receive units 40 and 60 of the lower and upper adjacentsub-channels.(D) General Configuration Example of Communication System of PresentInvention having Four Sub-Channels

FIG. 6 is a general block diagram depicting a communication system fordemodulating receive data using the interference between lower onesub-channel and upper two sub-channels, comprising four transmitters121, 122, 123 and 124 for transmitting data independently via foursub-channels, ch−1, ch0, ch+1 and ch+2, many cross-talk paths 131 _(ij)having the coupling coefficient α_(ij) from the i-th sub-channel to thej-th sub-channel, four receivers 150, 160, 170 and 180 which areinstalled for each sub-channel for receiving data from the correspondingsub-channel and performing soft decision for the receive data, and means191 and 192 for inputting the soft decision target value of eachreceiver to the receiver 160 of the target channel ch0. Means forinputting the other receivers is omitted in FIG. 6, but can be regardedas the same for the receiver 160. 132-139 and 140-143 are synthesizingunits for synthesizing ICI signals and noises.

The receiver 160 of the sub-channel ch0 adjusts its own soft decisiontarget value using the soft decision target values which were input fromthe receivers 150, 170 and 180 of the lower and upper sub-channels ch−1,ch+1 and ch+2, and decides “0” or “1” of the receive data based on thesoft decision target value. In the same way, the other receivers as welladjust their own soft decision target values using the soft decisiontarget values which were input from the receivers of the lower and uppersub-channels, and decides “0” or “1” of the receive data based on theadjusted soft decision target values.

(E) Receive Symbol Demodulation Algorithm in Four Sub-Channels

An algorithm for the receiver of the target sub-channel ch0 todemodulate the receive symbol in the communication system shown in FIG.6 will be described.

The principle of the demodulation algorithm is deriving the value InD₀,which indicates the difference between the posterior probability P(D₀=+1/y(t)) of the information symbol received by the targetsub-channel ch0 being “0” (=+1) and the posterior probability P(D₀=−1/y(t)) of the information symbol being “1” (=−1), just like thecase of the three sub-channel model. Since the probability differenceInD₀ of the target sub-channel is the difference between the posteriorprobability P (D₀=+1/y(t)) of the receive information symbol being “0”(=+1) and the posterior probability P (D₀=−1/y(t)) of the receiveinformation symbol being “1” (=−1), the receive information of thetarget sub-channel can be decided as “0” if ln D₀>0, and the receiveinformation of the target sub-channel is “1” if ln D₀<0.

It is assumed that binary information is transmitted as signalS*_(ij)(t) via two adjacent sub-channels. The index i in S*_(ij)(t)indicates the sub-channel number, and the index j is determined by thesign of the information symbol D_(i)(i=−1, 0 or 1) in the sub-channel i.In other words,

if D_(i)=+1, then j=0

if D_(i)=−1, then j=1

Hereafter to simplify notation, the time dependency of S*_(ij)(t) inexpressions is omitted. In other words, S*_(ij)(t) is denoted asS*_(ij).

As FIG. 6 shows, the signal of the target sub-channel affected by ICIfrom the lower and upper sub-channels is expressed as the linearcoupling of the signals S*_(−1j), S*_(1j) and S*_(2j) transmitted by theupper and lower sub-channels, and the target channel signal S*_(0j) bythe cross-talk coefficient α. The cross-talk coefficient α is a valueaccording to the leak of cross-talk. If the information symbol D₀ of thetarget channel is +1, then the receive signal S_(j) (j=0-7) of thetarget channel becomes

$\begin{matrix}\left\{ {\begin{matrix}{S_{0} = {S_{00}^{*} + {\alpha_{- 10} \cdot S_{- 10}^{*}} + {\alpha_{10} \cdot S_{10}^{*}} + {\alpha_{20} \cdot}}} \\{S_{20}^{*},{D_{0} = {+ 1}},{D_{- 1} = {+ 1}},{D_{1} = {+ 1}},{D_{2} = {+ 1}}} \\\begin{matrix}{S_{1} = {S_{00}^{*} + {\alpha_{- 10} \cdot S_{- 10}^{*}} + {\alpha_{10} \cdot S_{10}^{*}} - {\alpha_{20} \cdot}}} \\{S_{20}^{*},{D_{0} = {+ 1}},{D_{- 1} = {+ 1}},{D_{1} = {+ 1}},{D_{2} = {- 1}}}\end{matrix} \\\begin{matrix}{S_{2} = {S_{00}^{*} + {\alpha_{- 10} \cdot S_{- 10}^{*}} - {\alpha_{10} \cdot S_{10}^{*}} + {\alpha_{20} \cdot}}} \\{S_{20}^{*},{D_{0} = {+ 1}},{D_{- 1} = {+ 1}},{D_{1} = {- 1}},{D_{2} = {+ 1}}}\end{matrix} \\\begin{matrix}{S_{3} = {S_{00}^{*} + {\alpha_{- 10} \cdot S_{- 10}^{*}} - {\alpha_{10} \cdot S_{10}^{*}} - {\alpha_{20} \cdot}}} \\{S_{20}^{*},{D_{0} = {+ 1}},{D_{- 1} = {+ 1}},{D_{1} = {- 1}},{D_{2} = {- 1}}}\end{matrix}\end{matrix}\left\{ \begin{matrix}{S_{4} = {S_{00}^{*} - {\alpha_{- 10} \cdot S_{- 10}^{*}} + {\alpha_{10} \cdot S_{10}^{*}} + {\alpha_{20} \cdot}}} \\{S_{20}^{*},{D_{0} = {+ 1}},{D_{- 1} = {- 1}},{D_{1} = {+ 1}},{D_{2} = {+ 1}}} \\\begin{matrix}{S_{5} = {S_{00}^{*} + {\alpha_{- 10} \cdot S_{- 10}^{*}} + {\alpha_{10} \cdot S_{10}^{*}} - {\alpha_{20} \cdot}}} \\{S_{20}^{*},{D_{0} = {+ 1}},{D_{- 1} = {- 1}},{D_{1} = {+ 1}},{D_{2} = {- 1}}}\end{matrix} \\\begin{matrix}{S_{6} = {S_{00}^{*} + {\alpha_{- 10} \cdot S_{- 10}^{*}} - {\alpha_{10} \cdot S_{10}^{*}} + {\alpha_{20} \cdot}}} \\{S_{20}^{*},{D_{0} = {+ 1}},{D_{- 1} = {- 1}},{D_{1} = {- 1}},{D_{2} = {+ 1}}}\end{matrix} \\\begin{matrix}{S_{7} = {S_{00}^{*} + {\alpha_{- 10} \cdot S_{- 10}^{*}} - {\alpha_{10} \cdot S_{10}^{*}} - {\alpha_{20} \cdot}}} \\{S_{20}^{*},{D_{0} = {+ 1}},{D_{- 1} = {- 1}},{D_{1} = {- 1}},{D_{2} = {- 1}}}\end{matrix}\end{matrix} \right.} \right. & (32)\end{matrix}$depending on whether the signals D⁻¹, D₁ and D₂ of the lower and uppersub-channels are +1 or −1.j of the signal S_(j) indicates the signal number. In the same way, ifthe information symbol D₀ of the target channel is −1, then the receivesignal S_(j) (j=8-15) of the target channel becomes

$\begin{matrix}\left\{ {\begin{matrix}{S_{8} = {{- S_{00}^{*}} + {\alpha_{- 10} \cdot S_{- 10}^{*}} + {\alpha_{10} \cdot S_{10}^{*}} + {\alpha_{20} \cdot}}} \\{S_{20}^{*},{D_{0} = {- 1}},{D_{- 1} = {+ 1}},{D_{1} = {+ 1}},{D_{2} = {+ 1}}} \\\begin{matrix}{S_{9} = {{- S_{00}^{*}} + {\alpha_{- 10} \cdot S_{- 10}^{*}} + {\alpha_{10} \cdot S_{10}^{*}} - {\alpha_{20} \cdot}}} \\{S_{20}^{*},{D_{0} = {- 1}},{D_{- 1} = {+ 1}},{D_{1} = {+ 1}},{D_{2} = {- 1}}}\end{matrix} \\\begin{matrix}{S_{10} = {{- S_{00}^{*}} + {\alpha_{- 10} \cdot S_{- 10}^{*}} - {\alpha_{10} \cdot S_{10}^{*}} + {\alpha_{20} \cdot}}} \\{S_{20}^{*},{D_{0} = {- 1}},{D_{- 1} = {+ 1}},{D_{1} = {- 1}},{D_{2} = {+ 1}}}\end{matrix} \\\begin{matrix}{S_{11} = {{- S_{00}^{*}} + {\alpha_{- 10} \cdot S_{- 10}^{*}} - {\alpha_{10} \cdot S_{10}^{*}} - {\alpha_{20} \cdot}}} \\{S_{20}^{*},{D_{0} = {- 1}},{D_{- 1} = {+ 1}},{D_{1} = {- 1}},{D_{2} = {- 1}}}\end{matrix}\end{matrix}\left\{ \begin{matrix}{S_{12} = {{- S_{00}^{*}} - {\alpha_{- 10} \cdot S_{- 10}^{*}} + {\alpha_{10} \cdot S_{10}^{*}} + {\alpha_{20} \cdot}}} \\{S_{20}^{*},{D_{0} = {- 1}},{D_{- 1} = {- 1}},{D_{1} = {+ 1}},{D_{2} = {+ 1}}} \\\begin{matrix}{S_{13} = {{- S_{00}^{*}} - {\alpha_{- 10} \cdot S_{- 10}^{*}} + {\alpha_{10} \cdot S_{10}^{*}} - {\alpha_{20} \cdot}}} \\{S_{20}^{*},{D_{0} = {- 1}},{D_{- 1} = {- 1}},{D_{1} = {+ 1}},{D_{2} = {- 1}}}\end{matrix} \\\begin{matrix}{S_{14} = {{- S_{00}^{*}} - {\alpha_{- 10} \cdot S_{- 10}^{*}} - {\alpha_{10} \cdot S_{10}^{*}} + {\alpha_{20} \cdot}}} \\{S_{20}^{*},{D_{0} = {- 1}},{D_{- 1} = {- 1}},{D_{1} = {- 1}},{D_{2} = {+ 1}}}\end{matrix} \\\begin{matrix}{S_{15} = {{- S_{00}^{*}} - {\alpha_{- 10} \cdot S_{- 10}^{*}} - {\alpha_{10} \cdot S_{10}^{*}} - {\alpha_{20} \cdot}}} \\{S_{20}^{*},{D_{0} = {- 1}},{D_{- 1} = {- 1}},{D_{1} = {- 1}},{D_{2} = {- 1}}}\end{matrix}\end{matrix} \right.} \right. & (33)\end{matrix}$depending on whether the signals D⁻¹, D₁ and D₂ of the lower and uppersub-channels area +1 or −1.

After introducing ICI, S_(j) (j=0, 1, 2, . . . 15) is used as 16 signalsat the input of the receiver of each sub-channel. The index j of S_(j)in the expressions (32) and (33) indicates the signal number, and isdetermined by pairing the symbols D⁻¹, D₁, D₂ and D₀ in the lowersub-channel, upper sub-channel and target sub-channel.

By considering the following [1] and [2], the algorithm for optimumreception can be further developed. In other words, by considering [1]that the signs of some information signals are the opposite, that isS*⁻¹⁰=−S*⁻¹¹, S*₀₀=−S*₀₁, S*₁₀=−S*₁₁, and S*⁻²⁰=−S*₂₁, and [2] totransmit information signals a same signal is used for the lower, upperand target sub-channels, that is, S*⁻¹⁰=S*₀₀=S*₁₀=S*₂₀ andS*⁻¹¹=S*₀₁=S*₁₁=S*₂₁, the algorithm for optimum reception can be furtherdeveloped. The latter [2] indicates that all the sub-channels have thesame value and the information signals of all the sub-channels have nodifference in amplitude, waveform and energy. In this case, the signalsof the expressions (32) and (33) in each sub-channel become a pair,having opposite signs, as shown in the following expressions.S₀=−S₁₅, S₁=−S₁₄, S₂=−S₁₃, S₃=−S₁₂S₄=−S₁₁, S₅=−S₁₀, S₆=−S₉, S₇=−S₈  (34)

Hereafter this case can be considered in the same way as the threesub-channel model. In other words, just like the case of the threesub-channel model, the posterior probabilities P (D₀=+1/y(t)) and P(D₀=−1/y(t)) of the receive information symbol D₀ of the targetsub-channel becoming “0” (=+1) and “1” (=−1) are determined. If theseare determined, the sign (+1 or −1) of the receive symbol can bedetermined by comparing these values or comparing the difference of thelogarithms thereof and the threshold value. In other words, to determinewhether the information symbol D₀ of the target sub-channel is +1 or −1,

$\frac{P\left( {D_{0} = {{+ 1}/{y(t)}}} \right)}{P\left( {D_{0} = {{- 1}/{y(t)}}} \right)}$is computed first and compared with 1, and if the result is greater than1, it is decided that D₀=+1, and if the result is smaller than 1, it isdecided that

-   -   ln P (D₀=+1/y(t))−ln P (D₀=−1/y(t)) is computed and then the        negative or positive of the result is decided. In other words,        if positive it is decided that D₀=+1, and if negative it is        decided that D₀=−1. y(t) is a synthesized signal (y        (t)=S_(j)+n(t)) of the signal series S_(j) involving ICI and the        white Gaussian noise n (t) having spectrum power intensity N₀.

In the case of a four sub-channel model,

$\begin{matrix}{{\ln\mspace{14mu}{P\left( {D_{0} = {{+ 1}/{y(t)}}} \right)}} = {\frac{a + b}{2} + {\ln\mspace{14mu} 2} + {\ln\mspace{14mu}{\cosh\left( \frac{a - b}{2} \right)}}}} & (35) \\{{\ln\mspace{14mu}{P\left( {D_{0} = {{- 1}/{y(t)}}} \right)}} = {\frac{c + d}{2} + {\ln\mspace{14mu} 2} + {\ln\mspace{14mu}{\cosh\left( \frac{c - d}{2} \right)}}}} & (36)\end{matrix}$Here a, b, c and d are as shown in the following expressions.

$\begin{matrix}{a = {{\ln\mspace{14mu}{P\left( {D_{- 1} = {+ 1}} \right)}} + {0.5\begin{Bmatrix}{{\ln\mspace{14mu}{P\left( {D_{1} = {+ 1}} \right)}} + {\ln\left( {{P\left( {D_{2} = {+ 1}} \right)} \cdot} \right.}} \\{\left. {{P\left( {{y(t)}/S_{0}} \right)} + {{P\left( {D_{2} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{1}} \right)}}} \right) +} \\\begin{matrix}{{\ln\mspace{14mu}{P\left( {D_{1} = {- 1}} \right)}} + {\ln\left( {{P\left( {D_{2} = {+ 1}} \right)} \cdot} \right.}} \\\left. {{P\left( {{y(t)}/S_{2}} \right)} + {{P\left( {D_{2} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{3}} \right)}}} \right)\end{matrix}\end{Bmatrix}} + {\ln\mspace{14mu} 2} + {\ln\mspace{14mu}\cosh\left\{ {0.5 \cdot \begin{Bmatrix}\begin{matrix}{{\ln\mspace{20mu}{P\left( {D_{1} = {+ 1}} \right)}} - {\ln\mspace{14mu}{P\left( {D_{1} = {- 1}} \right)}} +} \\{\ln\mspace{14mu}\left\{ {{{P\left( {D_{2} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{0}} \right)}} +} \right.} \\{\left. {P{\left( {D_{2} = {- 1}} \right) \cdot {P\left( {{y(t)}/S_{1}} \right)}}} \right\} -}\end{matrix} \\{\ln\left( {{{P\left( {D_{2} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{2}} \right)}} +} \right\}} \\{{P\left( {D_{2} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{3}} \right)}}\end{Bmatrix}} \right\}}}} & (37) \\{b = {{\ln\mspace{14mu}{P\left( {D_{- 1} = {+ 1}} \right)}} + {0.5\begin{Bmatrix}{{\ln\mspace{14mu}{P\left( {D_{1} = {+ 1}} \right)}} + {\ln\left( {{P\left( {D_{2} = {+ 1}} \right)} \cdot} \right.}} \\{\left. {{P\left( {{y(t)}/S_{4}} \right)} + {{P\left( {D_{2} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{5}} \right)}}} \right) +} \\\begin{matrix}{{\ln\mspace{14mu}{P\left( {D_{1} = {- 1}} \right)}} + {\ln\left( {{P\left( {D_{2} = {+ 1}} \right)} \cdot} \right.}} \\\left. {{P\left( {{y(t)}/S_{6}} \right)} + {{P\left( {D_{2} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{7}} \right)}}} \right)\end{matrix}\end{Bmatrix}} + {\ln\mspace{14mu} 2} + {\ln\mspace{14mu}\cosh\left\{ {0.5 \cdot \begin{Bmatrix}\begin{matrix}{{\ln\mspace{20mu}{P\left( {D_{1} = {+ 1}} \right)}} - {\ln\mspace{14mu}{P\left( {D_{1} = {- 1}} \right)}} +} \\{\ln\mspace{14mu}\left\{ {{{P\left( {D_{2} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{4}} \right)}} +} \right.} \\{\left. {P{\left( {D_{2} = {- 1}} \right) \cdot {P\left( {{y(t)}/S_{5}} \right)}}} \right\} -}\end{matrix} \\{\ln\left\{ {{{P\left( {D_{2} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{6}} \right)}} +} \right.} \\\left. {{P\left( {D_{2} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{7}} \right)}} \right\}\end{Bmatrix}} \right\}}}} & (38) \\{c = {{\ln\mspace{14mu}{P\left( {D_{- 1} = {+ 1}} \right)}} + {0.5\begin{Bmatrix}{{\ln\mspace{14mu}{P\left( {D_{1} = {+ 1}} \right)}} + {\ln\left( {{P\left( {D_{2} = {+ 1}} \right)} \cdot} \right.}} \\{\left. {{P\left( {{y(t)}/S_{8}} \right)} + {{P\left( {D_{2} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{9}} \right)}}} \right) +} \\\begin{matrix}{{\ln\mspace{14mu}{P\left( {D_{1} = {- 1}} \right)}} + {\ln\left( {{P\left( {D_{2} = {+ 1}} \right)} \cdot} \right.}} \\\left. {{P\left( {{y(t)}/S_{10}} \right)} + {{P\left( {D_{2} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{11}} \right)}}} \right)\end{matrix}\end{Bmatrix}} + {\ln\mspace{14mu} 2} + {\ln\mspace{14mu}\cosh\left\{ {0.5 \cdot \begin{Bmatrix}\begin{matrix}{{\ln\mspace{20mu}{P\left( {D_{1} = {+ 1}} \right)}} - {\ln\mspace{14mu}{P\left( {D_{1} = {- 1}} \right)}} +} \\{\ln\mspace{14mu}\left\{ {{{P\left( {D_{2} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{8}} \right)}} +} \right.} \\{\left. {P{\left( {D_{2} = {- 1}} \right) \cdot {P\left( {{y(t)}/S_{9}} \right)}}} \right\} -}\end{matrix} \\{\ln\left\{ {{{P\left( {D_{2} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{10}} \right)}} +} \right.} \\\left. {{P\left( {D_{2} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{11}} \right)}} \right\}\end{Bmatrix}} \right\}}}} & (39) \\{c = {{\ln\mspace{14mu}{P\left( {D_{- 1} = {+ 1}} \right)}} + {0.5\begin{Bmatrix}{{\ln\mspace{14mu}{P\left( {D_{1} = {+ 1}} \right)}} + {\ln\left( {{P\left( {D_{2} = {+ 1}} \right)} \cdot} \right.}} \\{\left. {{P\left( {{y(t)}/S_{12}} \right)} + {{P\left( {D_{2} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{13}} \right)}}} \right) +} \\\begin{matrix}{{\ln\mspace{14mu}{P\left( {D_{1} = {- 1}} \right)}} + {\ln\left( {{P\left( {D_{2} = {+ 1}} \right)} \cdot} \right.}} \\\left. {{P\left( {{y(t)}/S_{14}} \right)} + {{P\left( {D_{2} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{15}} \right)}}} \right)\end{matrix}\end{Bmatrix}} + {\ln\mspace{14mu} 2} + {\ln\mspace{14mu}\cosh\left\{ {0.5 \cdot \begin{Bmatrix}\begin{matrix}{{\ln\mspace{20mu}{P\left( {D_{1} = {+ 1}} \right)}} - {\ln\mspace{14mu}{P\left( {D_{1} = {- 1}} \right)}} +} \\{\ln\mspace{14mu}\left\{ {{{P\left( {D_{2} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{12}} \right)}} +} \right.} \\{\left. {P{\left( {D_{2} = {- 1}} \right) \cdot {P\left( {{y(t)}/S_{13}} \right)}}} \right\} -}\end{matrix} \\{\ln\left\{ {{{P\left( {D_{2} = {+ 1}} \right)} \cdot {P\left( {{y(t)}/S_{14}} \right)}} +} \right.} \\\left. {{P\left( {D_{2} = {- 1}} \right)} \cdot {P\left( {{y(t)}/S_{15}} \right)}} \right\}\end{Bmatrix}} \right\}}}} & (40)\end{matrix}$

Finally ln D₀ is given by the following expression using the expressions(35) and (36).

$\begin{matrix}{{\ln\mspace{14mu} D_{0}} = {\frac{a + b}{2} - \frac{c + d}{2} + {\ln\mspace{14mu}\cosh\;\left( \frac{a - b}{2} \right)} - {\ln\mspace{14mu}{\cosh\left( \frac{c - d}{2} \right)}}}} & (41)\end{matrix}$(F) Receiver of the Present Invention

FIG. 7 and FIG. 8 are block diagrams depicting a receiver of the targetsub-channel of the present invention in the case when the cross-talkfrom upper two sub-channels and lower one sub-channel exist, which areseparated in the figures by a dash and dotted line, and implements thecomputation of the right side member of the expression (41). FIG. 7shows the configuration of the left side of the receiver, and FIG. 8shows the right side thereof. If the receiver in FIG. 7 and FIG. 8 isthe receiver of the target channel ch0, this receiver has aconfiguration combining the receiver of the three sub-channel modelwhich receives cross-talk from the channels ch+1 and ch+2, and thereceiver of the two sub-channel model which receives cross-talk from thechannel ch1, and the expression (41) becomes the sum of the values atthe points P1, P2 and P3 in FIG. 7 and FIG. 8.

The receiver 160 of the target sub-channel comprises a correlation unit161, first-third computing units 162-164, synthesizing unit 165 anddecision unit 166. In the figures, ∫dt is an integrator for computing

$\frac{2}{N_{0}}{\int_{o}^{T}{{{y(t)} \cdot {S_{i}(t)}}{{\mathbb{d}t}.}}}$lnD_(i)=ln P (D_(i)=+1)−ln P (D_(i)=−1) is the logarithmic difference ofthe posterior probabilities of the signal Di transmitted by the i-thsub-channel (i=−1, +1, +2) becoming +1 or −1 (soft decision value in thei-th sub-channel). Here the energy of the signal S_(j) (t) is E_(j),which is given by

E_(j) = ∫₀^(T)S_(j)²(t)𝕕t.Also

${{\Delta\; E_{\Sigma}} = \frac{E_{0} + E_{1} - E_{2} - E_{3}}{N_{0}}},{{\Delta\; E_{\Sigma}} = \frac{E_{4} + E_{5} - E_{6} - E_{7}}{N_{0}}},{{\Delta\; E_{\Sigma}} = \frac{E_{0} + E_{1} + E_{2} + E_{3} - E_{4} - E_{5} - E_{6} - E_{7}}{N_{0}}}$${{\Delta\; E_{0}} = \frac{E_{0} - E_{1}}{N_{0}}},{{\Delta\; E_{2}} = \frac{E_{2} - E_{3}}{N_{0}}},{{\Delta\; E_{4}} = \frac{E_{4} - E_{5}}{N_{0}}},{{\Delta\; E_{6}} = \frac{E_{6} - E_{7}}{N_{0}}}$

The correlation unit 161 is comprised of the computing units (multiplierand integrator) for computing

$\frac{2}{N_{0}}{\int_{o}^{T}{{{y(t)} \cdot {S_{0}(t)}}{\mathbb{d}{\left. t \right.\sim\frac{2}{N_{0}}}}{\int_{o}^{T}{{{y(t)} \cdot {S_{7}(t)}}{\mathbb{d}t}}}}}$and the addition/subtraction circuit for computing S₀′+S₁′, S₀′−S₁′,S₂′+S₃′, S₂′−S₃′ . . . , ΣS_(j)′ (j=0-7) when

$\frac{2}{N_{0}}{\int_{o}^{T}{{{y(t)} \cdot {S_{0}(t)}}{\mathbb{d}{\left. t \right.\sim\frac{2}{N_{0}}}}{\int_{o}^{T}{{{y(t)} \cdot {S_{7}(t)}}{\mathbb{d}t}}}}}$are expressed as S₀′, S₁′, S₇′ respectively.

The first computing unit 162 has a configuration the same as theconfiguration enclosed by a dash and dotted line in FIG. 5, and computesthe second-fifth terms of the right side member of the expression (28)and expressions (29) and (30) for the signals S₀ (t), . . . S₃ (t) outof the signals S₀ (t), S₁ (t), . . . S₇ (t). In the addition unit 165 aof the synthesizing unit 165, the first term of the right side member(=S₀′+S₁′+S₂′+S₃′) of the expression (28) is added, and computation ofthe expression (29) completes.

The second computing unit 163 has the same configuration as theconfiguration enclosed by the dash and dotted line in FIG. 5, andcomputes the second to fifth terms of the right side member of theexpression (28) and the expressions (29) and (30) for the signals S₄(t), . . . S₇ (t) out of the signals S₀ (t), S₁ (t), . . . S₇ (t).However in the expressions (28), (29) and (30), S₀ (t) . . . S₃ (t) arereplaced with S₄ (t) . . . S₇ (t). In the addition unit 165 a of thesynthesizing unit 165, the first term of the right sidemember(=S₄′+S₅′+S₆′+S₇′) of the expression (28) is added, andcomputation for the expression (29) completes.

The synthesizing unit 165 synthesizes the computing result of the rightside member of the expression (27) for the signals S₀ (t) . . . S₃ (t),that is

$\begin{matrix}{\frac{A + B}{2} - \frac{C + D}{2} + {\ln\mspace{20mu}{\cosh\left( \frac{A - B}{2} \right)}} - {\ln\mspace{20mu}{\cosh\left( \frac{C - D}{2} \right)}}} & (42)\end{matrix}$and the computing result of the right side member of the expression (27)for the signals S₄ (t) . . . S₇ (t), that is

$\begin{matrix}{\frac{A^{\prime} + B^{\prime}}{2} - \frac{C^{\prime} + D^{\prime}}{2} + {\ln\mspace{20mu}{\cosh\left( \frac{A^{\prime} - B^{\prime}}{2} \right)}} - {\ln\mspace{20mu}{\cosh\left( \frac{C^{\prime} - D^{\prime}}{2} \right)}}} & (43)\end{matrix}$and adds the computing result of the third computing unit 164 to thesynthesized result (value at the point P1 in the figure), and inputs itto the decision unit 166 as ln D₀ of the expression (41).

The third computing unit 164 corrects the computing result based on thesoft decision data ln D⁻¹ of the lower sub-channel ch−1, and performspredetermined computation on the correction result, and inputs it to thesynthesizing unit 165.

If the values of the first-fifth terms of the expression (28) for thesignals S₀ (t), S₁ (t), S₂ (t) and S₃ (t) are expressed as {circlearound (1)}-{circle around (5)}, the values of the first-fifth terms ofthe expression (28) for the signals S₄(t) S₅ (t), S₆ (t) and S₇ (t) areexpressed as {circle around (1)}′-{circle around (5)}′, and the outputof the soft decision data ln D⁻¹ operating unit 164 a is expressed as{circle around (6)}, then the value of the point P2 becomesln cosh(½)·[{({circle around (2)}+{circle around (4)}−{circle around(2)}′−{circle around (4)}′)/2+{circle around (6)}−ΔΣ_(Σ)}+ln cosh{(A−B)/2}−ln cosh{(A′−B′)/2}]  (44)and the value of the point P3 becomesln cosh(½)·[{({circle around (3)}′+{circle around (5)}′−{circle around(3)}−{circle around (5)})/2+{circle around (6)}+ΔΣ_(Σ)}+ln cosh{(C′−D′)/2}−ln cosh{(C−D)/2}]  (45)Therefore ln D₀ (soft decision target value) after synthesizing thevalues of the points P1, P2 and P3, that is ln D₀ (soft decision targetvalue) given by the expression (41) is input to the symbol decision unit166. Here ln D₀=(42)+(43)+(44)+(45).

The symbol decision unit 166 decides the positive/negative of the ln D₀(soft decision target value), and if positive the receive symbol isdecided as “0”, and if negative it is decided as “1”. Also the symboldecision unit 166 feeds back the in D₀ (soft decision target value) tothe decision result operating unit of the receive units 150, 170 and 180of the lower and upper sub-channels.

As described above, in the multi-carrier communication system fortransmitting/receiving signals via at least four sub-channels, thereceiver of the target sub-channel ch0 adjusts its own bit decisiontarget value ln D₀ using the soft decision target values ln D₊₁, ln D₊₂and ln D⁻¹, in the sub-channels other than the target sub-channel, anddecides the receive data based on this soft decision target value.

(G) Similarity with a Turbo Decoder

The above mentioned demodulation algorithm of the receive data of thepresent invention is similar to the turbo decoder of the turbo codeswritten in the following document.

Document: M. C. Valenti and B. D. Woerner: “Variable latency turbo codesfor wireless multimedia applications”, Proc. Int. Symposium on Turbocodes and Related Topics, Brest, France, September 1997, pp. 216-219.

Because of the similarity with the turbo decoder, let us call thealgorithm of the present invention a “turbo receiver“. In the turbodecoder, each decoder transfers the information to the other decoders,and refines the estimated posterior probability sequentially using theinformation derived by the other decoders. In the same way, in thealgorithm of the present invention as well, the information derived fromone sub-channel is used to refine the estimated posterior probability ofthe other channel after non-linear processing, and the informationderived from the latter sub-channel is used to refine the estimatedposterior probability of the former channel. If an individual decoderoutput is hard bit decision (hard decision) format in the turbo decoder,sharing information has few advantages. A hard bit decision is similarto the decision feedback equalizer proposed by Viterbo and Fazel in theabove mentioned Document 2 for canceling ICI. Here the hard bit decisionis executed only at the end of a repeat.

This structural similarity is because of the following reasons. In otherwords, in the turbo receiver, just like the case of turbo codes, thesame information is transmitted on the sub-channel having unrelatednoise due to the presence of ICI. Depending on the behavior of thisunrelated noise, the estimation (or the reliability of the decision of)posterior probability can be improved using the estimated posteriorprobability derived from other sub-channels.

Just like the case of the repeat turbo decoder, the algorithm of thepresent invention performs one or more repeats before the final decisionfor the received information. If the data is an equally distributedprobability variable at the first step, that is when a decision fromother channels cannot be used,P(D ⁻¹=+1)=½, P(D ⁻¹=−1)=½P(D ₊₁=+1)=½, P(D ₊₁=−1)=½P(D ₊₂=+1)=½, P(D ₊₂=−1)=½can be set for the first sub-channel. This setting is the best.Therefore in the first step, the difference ln D⁻¹ of the posteriorprobabilities in the low sub-channel ch−1 is regarded as 0. According tothe same concept, in the upper sub-channels ch+1 and ch+2, thedifference of the posterior probabilities is regarded as ln D₊₁=0 and lnD₊₂=0. By calculating the expressions (35)-(36) and (41), assuming lnD⁻¹=ln D₁=ln D₂=0, the first estimate of ln D₀, which was unknown, canbe acquired. In the same way, in an N sub-channel communication system,the lower sub-channel computes ln D⁻¹ assuming ln D⁻²=ln D₀=ln D₁=0, andthe upper sub-channel computes ln D₁ assuming ln D₃=ln D₂=ln D₀=0 at thefirst repeat according to the algorithm of the present invention. In thesecond step, ln D⁻¹, ln D₁ and ln D₂ acquired in the previous step areapplied to the decision expressions (35)-(36) and (41) to compute thenew estimate value of the posterior probability of the targetsub-channel. By this, the output of one sub-channel receiver is used asthe prior probability for the other receivers.

FIG. 9 shows the constellation of the target channel in thecommunication system where N=64, and is a case when QPSK modulation withthe S/N ratio=20 dB is performed after a different number of times ofrepeats. The cross channel leak coefficient here is α⁻¹⁰=0.25, α₁₀=0.15and α₂₀=0.075. (A) is QPSK modulated original data, (B) are signalsdeteriorated by ICI, (C) is a receive signal with an S/N ratio=20 dB,(D) is the receive data after one repeat according to the presentinvention, and (E) is the constellation of the receive data after thesecond repeat according to the present invention.

As shown here, according to the present invention, the dispersion inconstellation is small, and the BER is improved to become smaller. Asthe number of repeats increases, the dispersion in constellationdecreases further, and BER is further improved.

(H) Noise Immunity and Simulation Results

In order to prove the validity of the non-linear signal processing ofthe present invention, computer simulation was performed for thereceiver of the present invention and conventional matched filterreceiver. FIG. 10 shows the average BER performance in the receiver ofthe present invention, and the matched filter receiver as a function of2Eb/N₀ in the case of α⁻¹⁰=0.25, α₁₀=0.15 and α₂₀=0.075 (see simulationresults A-D). Eb/N₀ is a ratio of the average receive signal energy Ebagainst the background noise power spectrum intensity N₀ per bit. As areference, the simulation result E of the receiver of the presentinvention in the case of α⁻¹⁰=α₁₀=α₂₀=0 without ICI (equivalent to thematched filter receiver), is shown in FIG. 9. Also as a reference, theBER simulation result F of the matched filter receiver when ICI does notexist, which was calculated using the expression (46), is shown.

$\begin{matrix}{P_{err} = {{\frac{1}{2} \cdot {erfc}}\text{(}\sqrt{0.5 \cdot {SNR}}}} & (46)\end{matrix}$where erfc

$(x) = {{{erfc}(x)} = {{1 - {{erf}(x)}} = {\frac{2}{\sqrt{\pi}}{\int_{x}^{\infty}{{\mathbb{e}}^{- t^{2}}{\mathbb{d}t}}}}}}$

The BER performance acquired by computer simulation and the BERperformance calculated using the expression (46) match well. As the plotin FIG. 10 shows, the BER of the receiver of the present invention isnot different from the BER of the conventional matched filter basereceiver acquired using the expression (46) if ICI does not exist. Thelatter BER is indicated as “Reference” (E) in FIG. 10. When ICI exists(in the case of α₀₁=0.25, α₀₋₁=0.15 and α₂₀=0.075), the performance ofthe conventional device (repeat once, characteristic A), which does notperform non-linear processing, is not as good as the receiver of thepresent invention, and this is particularly obvious in a high Eb/N₀, asthe simulation results shows.

(I) Application to DMT System

As an application of the turbo receiver of the present invention, a DMTbase communication system is considered. FIG. 11 is a block diagramdepicting the DMT base communication system using this turbo receiver,and has a configuration where the turbo receiver of the presentinvention is disposed in the subsequent stage of the FFT section of thereceiver in a known DMT communication system.

In the communication system in FIG. 11, the input beam stream with datarate R (bits/sec: bps) is transferred at the new rate R/N (bps) afterthe serial-parallel converter (S/P) 201 through N number of parallelsub-channels. The N point IFFT 202 combines the N parallel data andconverts it into one set of real-time domain sample signals. In theparallel-serial converter (P/S) 203, these N samples are converted intoa serial format, and are continuously input into the digital-analogconverter (DAC) 204. The output signal of the low pass filter (LPF) 205at the DAC output side is the duration DMT signal. In the white Gaussiannoise channel, the transmission DMT signal is deteriorated by the whiteGaussian noise n(t) and is sent to the DMT receiver 300. The receiverexecutes a function the opposite of the transmitter. The FFT 301performs demodulation processing for the signals sent via eachsub-channel as N matched filter arrays. The turbo 302 ₁-302 _(N) performsub-channel processing based on the turbo algorithm of the presentinvention, and by this, BER improves even if a frequency offset exists.303 is the AD converter, 304 is the serial-parallel converter and 305 isthe parallel-serial converter.

FIG. 12 shows the BER performance of a conventional DMT base receiverand the BER performance of a DMT receiver which has the turbo processingfunction of the present invention, and performs three times and sixtimes of turbo repeats. In FIG. 12, a case of N=64 is shown, and the BERperformance is shown for 2Eb/N₀ using a frequency offset normalized byan inter-channel frequency as a parameter, and “proposed” is indicatedby the BER characteristic B and B′ (ICI-four model) of the presentinvention.

As FIG. 12 shows, the BER characteristic improves as the frequencyoffset becomes smaller, and the BER characteristic is better in the“ICI-four model” of the present invention than the conventional device.In the case of the proposed “ICI-three model” (characteristics A andA′), the BER characteristic improves for 2 dB.

As described above in the multi-carrier communication system, the effectof ICI on adjacent sub-channels was studied. The performance of aconventional matched filter receiver rapidly deteriorates as thecoupling of adjacent sub-channels increase or as the frequency offsetincreases. Whereas the present invention is a receiver based on anestimated posterior probability, and a receiver of each sub-channel is aturbo receiver for transferring information to the receivers of theadjacent sub-channels, and refines the estimated posterior probabilityusing the information derived by the receivers of the adjacentsub-channels repeatedly. Therefore the turbo receiver of the presentinvention can improve BER performance considerably compared with aconventional matched filter receiver. This is because the non-linearsignal processing of the turbo algorithm of the present invention usesthe information acquired by the adjacent sub-channels so as to maximizethe posterior probability. The biggest improvement in BER is generatedin a high S/N ratio area where ICI dominates Gaussian noise. Accordingto the simulation results, the turbo receiver of the present inventioncan achieve good performance throughout a considerably wide rage of ICIcoupling coefficients.

1. A multi-carrier communication system for transmitting/receivingsignals via at least four sub-channels, comprising: a transmitter fortransmitting data independently via the four sub-channels; a receivercomprising a receive unit disposed for each sub-channel for receivingdata from a corresponding sub-channel and performing soft decision ofthe receive data; and means for inputting soft decision target values inreceive units corresponding to three sub-channels other than a targetsub-channel to a receive unit of the target sub-channel, wherein thereceive unit of the target sub-channel adjusts its own soft decisiontarget value using the soft decision target values that are input fromthe receive units of the other sub-channels, and decides the receivedata based on the adjusted soft decision target value.
 2. Thecommunication system according to claim 1, wherein the receive unit ofsaid target sub-channel further comprises: means for computing adifference between a probability that the data received from the targetsub-channel is one of a binary and a probability that the data is theother of a binary as said soft decision target value, considering degreeof coupling of cross-talk paths; means for adjusting the soft decisiontarget value of the target sub-channel using said soft decision targetvalues that are input from the receive units of the three sub-channelsother than the target sub-channel; and a decision unit for deciding thereceive data based on said adjusted soft decision target value.
 3. Thecommunication system according to claim 1, wherein the receive unit ofsaid target sub-channel further comprises: means for creating first toeighth reference signals to be calculated considering cross-talk fromthe three sub-channels other than the target sub-channel in each of atotal of eight data combinations of the case when all the data of thethree data items transmitted by the three sub-channel signals are thesame, and the cases when at least one data item is different; eightcorrelation means for integrating the result of multiplication betweeneach reference signal and the actual receive signal respectively; meansfor generating the soft decision target value of the target sub-channelusing each correlation unit output and said soft decision target valuesthat were input from the receive units of the three sub-channels otherthan the target sub-channel; and a decision unit for deciding thereceive data based on the soft decision target value.
 4. Themulti-carrier communication system according to claim 3, wherein saidreceive unit is installed in the subsequent stage of an FFT constitutingthe DMT communication system.
 5. A receiver in a multi-carriercommunication system for transmitting data independently via at leastfour sub-channels, comprising: a receive unit disposed for eachsub-channel for receiving data from a corresponding sub-channel andperforming soft decision of the receive data, wherein the receivecomprises: soft decision target value output means for computing adifference between a probability that data received from its ownsub-channel is one of a binary and a probability where said data is theother of a binary as a soft decision target value, considering thedegree of coupling between channels, and adjusting and outputting thesoft decision target value of said sub-channel using soft decisiontarget values that are input from the receive units of the other threesub-channels; and a decision unit for deciding the receive data based onsaid adjusted soft decision target value.
 6. The receiver according toclaim 5, wherein said soft decision target value output means furthercomprises means for creating first to eighth reference signals to becalculated considering cross-talk from said three sub-channels in eachof a total of eight data combinations of the case when all the data ofthree data items transmitted by the three sub-channel signals are thesame, and the cases when at lest one data item is different; eightcorrelation means for integrating the result of multiplication betweeneach reference signal and the actual receive signal respectively; andmeans for generating the soft decision target value of the targetsub-channel using each correlation unit output and said soft decisiontarget values that are input from the receive units of said threesub-channels.